Welcome to Smogon, Razor720.
As Yip notes, the record list on the first page is probably your best bet for detailed team ideas and explanations of how the pokes on a well-made team work together. But I'll give some more suggestions here.
First, the absolute best streaks tend to be based on crippling the opposing lead (with passing a Choice Scarf, lowering its attacking stats, and/or using Entrainment to pass the Truant ability onto it). Since the AI only switches out in a very limited set of circumstances, a crippled lead then lets you bring in a sweeper to use a bunch of stat boosting and protective (Substitute) set up moves and then sweep the opposing team.
You can, however, put together very good streaks with more traditional synergy/attacking teams, and especially when you are just starting to learn the Subway, these are the types of teams you should try. They also tend to go through battles much faster than do cripple teams, which is a nice advantage. Ideally you'll want one hard hitter that can KO a lot of opposing pokes on its own, one bulky pivot that can help handle the pokes that your primary sweeper can't handle, and a third poke, bulky or hard hitting, to help fill in the gaps. To the extent possible, you'll want the pokes to cover each other's weakness and not share too many weakness between them, since all it takes is a team weakness to a single opposing poke to have your whole streak end abruptly. The front page gives some excellent team ideas, but on the subject of good individual pokes, here is a list of tried-and-true Subway pokes and their main advantages and disadvantages. Note that I'm not discussing dedicated cripplers here, but if you are interested in a crippling team, look at the front page for top scoring teams with Durant and/or Whimsicott and/or Latias, the most common and best Subway cripplers.
Garchomp: Amazing typing, and with a Jolly nature and max Speed, can outrun a large portion of the Subway. Garchomp's Ground and Dragon STABs cover a huge fraction of the Subway pokemon, and corner case moves like Fire Fang and Rock Slide can handle the few that they don't. With just a Choice Band, Garchomp's Outrange and Earthquake can OHKO a bunch of things, and with its only weaknesses being to Ice and Dragon moves, even where Garchomp isn't able to OHKO the opponent, most opponents won't be able to OHKO it either. Alternatively, you can run Swords Dance and Life Orb or Lum Berry and have Garchomp play as a set-up sweeper. Very few things can survive Garchomp's attacks at +2. Garchomp also plays very well with bulky Waters. It is immune to the Electric attacks that they draw, while they resist the Ice attacks that destroy it. Note that like any Dragon, it fears faster Dragon attacks, so you may also want a Steel to help protect against opposing Latios and Latias or Choice Scarf Garchomp.
Cloyster: After a single Shell Smash, Cloyster becomes an extremely fast and hard hitting beast. With Skill Link as its ability, Icicle Spear and Rock Blast both always hit 5 times, doing a ton of damage and breaking through both Focus Sashes and the Sturdy ability. Surf or Razor Shell provides additional coverage. Since Shell Smash lowers Cloyster's defenses, a typical tactic is to put it in the lead spot but equip it with a Focus Sash to ensure it survives the set up turn. Cloyster dislikes opposing priority and status ailments, particularly paralysis, so it pairs well with Garchomp or other Ground pokes, which can switch it on a predicted opposing first turn Thunder Wave.
Dragonite: Dragonite hits really hard, particularly after it gets in a Dragon Dance or two. Thanks to its Dream World ability of Multiscale, it is extremely hard to OHKO a Dragonite, buying it the time it needs to get at least one Dragon Dance in. After just one Dance, Dragonite outspeeds and OHKOs a lot of the Subway, and after a second, very few things can survive it, absent a Focus Sash or Sturdy. An equipped Lum Berry can both protect against the confusion from Outrage and allow you to Dragon Dance safely even in the face of a status move from the opponent. Dragonite is really versatile, as well. Outrage is its bread and butter for smashing holes in things, but even without STAB, Earthquake hits quite hard, especially against the Steels that resist Outrage. Fire Punch is another good coverage option. Roost lets Dragonite play a tankier role, and try to abuse Multiscale multiple times, while ExtremeSpeed can finish off frail but fast or priority-using opponents. For cripple teams, a mono-attacking Dragon Claw/Roost/Substitute/Dragon Dance Dragonite is probably the best sweeper available, once your other pokes have crippled the opponent to let you set up. Dragonite's biggest weakness is its low base speed. Because most other Subway Dragons can initially outspeed it, an unboosted Dragonite can take a lot of damage from an opposing lead Dragon. Lots of Ice move users can outspeed you too. You'll definitely want a Steel to switch in if you use Dragonite on a non-crippling team.
Suicune: My vote for best self-supporting poke in the Subway. Even without any team support, a Bold defensive Suicune can switch into and set up on a really large number of Subway pokes. Water is an amazing defensive type, and coupled with Suicune's big defenses, Suicune can be very tough to take down. A Scald/Calm Mind/Substitute/Rest set with Leftovers or a Chesto Berry is probably your best bet, but Ice Beam and Icy Wind are other move options to consider. Note that Pressure, a normally unexciting ability, is pure gold on Suicune. Many pokes have only one move that can break a Suicune Substitute, particularly after a Calm Mind or two, and Pressure lets you stall out that move, and then easily set up to +6/+6. Suicune lacks the reliability of Recover or the like, but given its tremendous bulk, it does just fine with Rest.
Milotic: If you lack a Suicune (or don't have one with good stats/nature), Milotic is your next best bet. Good bulk (particularly with Marvel Scale), reasonable speed, and the flexibility to attack decently well make Milotic a fine choice for a bulky Water in the Subway. Recover provides reliable recovery, Scald and Ice Beam give solid damage (and the chance of a super helpful burn or freeze), and Toxic lets you beat other bulky Waters (or bulky pokes generally). Some teams even add protect to the Toxic + Recover combo to crank up their Toxic Stalling. Milotic is vulnerable to untimely crits (since it doesn't normally have room to run Substitute) and unlike Suicune, can't set up on things it dominates to make sweeping subsequent pokes easier, but it can still serve you well.
Scizor: Excellent typing leaves it with only one weakness and a lot of key resistances, including both Ice and Dragon, and with Technician, its STAB moves Bug Bite and Bullet Punch hit hard. Can play a boosting tank type role with Roost and Swords Dance, or can use moves like Superpower for better coverage. Scizor can switch into a lot of scary moves thanks to its typing, and especially after a Swords Dance, can take big advantage of priority Bullet Bunch to kill a number of pokes before they can act. If you are using a Dragon, you'll likely want a Steel to cover its weaknesses, and Scizor is one of the best options available. Just make sure you're not otherwise weak to Fire, since that 4x weakness hurts!
Ferrothorn: Very bulky on both the physical and special sides, and its Grass typing removes the Ground weakness that most Steels hate. Because of its slow Speed, Ferrothorn's Gyro Ball can be extremely powerful, and Curse plays beautifully with it, not only boosting Ferrothorn's Attack and Defense, but also increasing Gyro Ball's power by dropping Speed. Ferrothorn can play a defensive stall role with Leech Seed and Substitute, or can broaden its attacking options with Power Whip. Ferrothorn's biggest disadvantages are that it lacks a reliable recovery move and its slow speed sometimes limits what it can set up on. The 4x Fire weakness hurts too. Still, Ferrothorn stops a number of big threats cold, and makes another good choice of Steel type.
Gengar: Gengar has a wonderful Special Attack stat and great Speed, enabling it to outrun threats like Infernape and the Musketeers. Its three immunities are really helpful too, and a small number of pokemon in the Subway are unable to hurt Gengar at all. Unfortunately, it lacks a good boosting move and with the limited power/coverage of its STAB moves, a Life Orb or Choice Specs set won't grab as many OHKOs as you might want. Accordingly, Gengar works best as a lead with a Focus Sash, 3 damaging attacks, and Destiny Bond. Against many foes, you can outspeed and 2HKO the lead, surviving the first-turn counter attack thanks to your Sash, and then outspeed and KO the second opponent with Destiny Bond. This leaves you with a 2-1 advantage, typically a happy place to be in a battle. Even where you can't beat the opponent's lead, you can almost always at least trade with it thanks to Destiny Bond, meaning Gengar always helps a little. Since Gengar usually dies, however, you need to be really sure your remaining two pokes can cover as broad a range of threats as possible, since if the opponent's last poke can beat both of Gengar's partners, you will be in trouble.
Starmie: 115 base Speed means that Starmie outruns the vast majority of Subway opponents. Coupled with Starmie's wonderful mix of coverage moves, and you've got a pokemon that can outrun and kill a number of opponents by hitting their weaknesses hard, particularly when equipped with a Life Orb or Choice Specs. Starmie can be a nice cleaner too, finishing off a pokemon that one of its teammates weakened. Natural Cure is a great ability, allowing Starmie to heal status with ease. Unfortunately, Starmie's Special Attack stat isn't anything special, and it lacks a boosting move, so if it can't hit a weakness, it probably isn't going to OHKO, and bulky foes will sometimes be able to survive hits on their weaknesses too. Still the combination of excellent coverage and Speed can make Starmie a valuable asset (and one of the most dangerous foes) in the Subway.
Latios: Not quite as fast as Starmie, but blessed with a much better Special Attack, Latios hits fast and hard. Latios also has the possibility to set up a bit with Calm Mind, letting it better muscle through opposing teams. You'll almost certainly want to run Dragon Pulse, but after that, you've got a lot of move flexibility, with a STAB Psychic or Psyshock, Thunderbolt, Surf, Ice Beam, and even Hidden Power Fire all being possibilities. You also have the option to use Latios as a hybrid attack-cripple lead, giving it three attacks, Life Orb, and Memento. Attack away until you get low, then Memento to make it easier for your next poke to set up. Psychic typing gives Latios a lot more weaknesses than the typical Dragon, but it has a nice resistance spread too, and is one of the few Dragons to lack the ugly 4x Ice weakness, which means it can survive medium strength Ice attacks where many of its brethren would crumble. Latios' biggest shortcoming compared to other Dragon-types is the lack of a special attacking version of Outrange. Dragon Pulse is a fine move, but the thirty points of power it lacks compared to Outrage often makes the difference between a OHKO and a 2HKO. Latios can get a lot of opponents low with one move, but can't blast through teams as well as an Outraging Garchomp or Dragonite. Draco Meteor looks nice, but the ninety percent accuracy can bite you at the worst possible time, and the minus two Special Attack drop means you can't use it to sweep whole teams. I've often wanted to run Choice Scarf Modest Latios as a cleaner and revenge killer alongside Garchomp, but it's hard to support a team with two Dragons, thanks to the shared weaknesses. Still, if you are in the market for a hard-hitting Dragon, Latios will serve you well.
Darmanitan: Sheer Force + Flare Blitz gives Darmanitan ridiculous power. Throw on a Choice Scarf and you'll outspend most of the Subway, while with a Choice Band, the power of your Flare Blitz will dwarf even that of Choice Band Garchomp's Outrage. Either way, Darmanitan can smash through many opponents with ease. Moves like Earthquake, Rock Slide, and Superpower give you reasonable coverage options, and U-Turn lets you do a little damage while switching out of unfavorable matchups. Still, spamming Flare Blitz is your biggest strength, and that alone will get you a number of wins. Another small advantage possessed by Darmanitan is that it is one of the easiest pokes on this list to acquire in-game. Your biggest weakness is that Fire doesn't have the greatest coverage and is a bad defensive type, but for pure attacking power, very little matches Darmanitan in the Subway.
This list is far from comprehensive, and there are plenty of other great options, but it should provide you with a nice starting place for building a non-crippling Subway team.
A few other general notes:
Take advantage of the lists of what pokemon different computer trainers use. Serebii has a nice and easy-to-use battle Subway trainer catalogue which you can easily google, and Team Rocket Elite and R Inanimate put together a similar resource here:
http://www.smogon.com/ingame/bc/bw_subway_trainers Just knowing the moveset and stats of the pokemon you are facing is ridiculously helpful.
EVs, IVs, and Nature really matter. All opposing pokes either max EVs in two stats or split them evenly between three, and very early on in a Subway run, they'll all have perfect IVs, too. This means that if you use pokemon with suboptimal natures, or bad EVs and IVs, you'll be at a disadvantage. For attacking pokes, you'll want to make sure that at the very least, you have the maximum IV in Speed, and having a maximum IV in the appropriate attack stat is highly recommended too. Garchomp, for example has 102 base Speed. With a Jolly nature and 31 IVs in Speed, plus 252 EVs, he'll outrun all non-boosted base-100s, even those with a speed-improving nature. But with just a slightly lower Speed IV, or a different nature, or less than the full 252 EVs, he'll no longer outspeed them all, and risk being outsped and killed by things that he should outrun. In general, for an attacking pokemon, you'll want a Speed-improving nature unless it's using a Choice Scarf or has a way to boost its Speed, like Dragon Dance. This isn't an absolute rule, but if you look at top non-crippling teams, you'll see that it is typically the case. Bulky pokes can often get away with lower IVs in Speed and Attack, but are much more dependent on having reasonable defensive stats. Obviously, RNGing is the easiest way to get well-IVed Subway pokes, but with breeding items and the like, it's not particularly difficult to manually breed a poke with 2 or 3 perfect stats either. Take the time to do so. It is worth it.
Finally take a look at this article on Subway basics by flavor0 and Cradily.
http://www.smogon.com/ingame/bc/battle_subway_part1
Hope this helps, and good luck putting a nice streak together.
PS: Make sure you have an answer to Timid King's Rock Starmie with Surf, Psychic, Ice Beam, and Thunderbolt. It is the bane of many a Subway team!!