Okay so I am going to have a whole bunch of stuff in this thread because I have trained so many teams across SO many games.
Instead of putting down everything, I'm going to put in my "original" teams for each game and then highlight some of my favourite teams I have used. It's going to be a long one because I've got to try and remember all those years back to make up some of the teams I used.
1999: Red
Oh man was I a Noob back then. Pretty sure my first team was something along the lines of:
Blastoise was an will always be one of my favourite Pokemon. He saved me more times than I can count during the game. All the others are pretty self explanatory really. My brother used Vaporeon, so by default almost I went with Jolteon (and my small affinity for the Electric Type). Articuno replaced Pidgeot as my bird of choice, Zapdos also was in this slot too. Omastar and Snorlax rounded out the team with a strong Water and an amazing Normal type.
2001: Gold
Gold is what got me really hooked on Pokemon. Day Night cycles and different Pokemon at different times of the day felt like an appropriate and logical step for Pokemon to make. I made a bit of a booboo here as my brother had used Bulbasaur in Blue, and I thought I'd give the grass type a try this time around... How wrong I was.
Pretty solid team all round... Apart from me failing at Jasmine and having trouble with Chuck. I didn't understand Steel at all until Quagsire came to the rescue with Surf... This team was actually pretty strong in the end... Meganium actually started to hold itself up.
2003: Sapphire
Into 3rd gen and I was understanding how to construct and use balanced teams. This is way before I started doing runs for the sake of playing the game. But I found some excellent Pokemon in Hoenn.
Pretty standard RS team I think. Swampert for obligatory Starter and every other mon is pretty much have to use for a first RS game. Hariyama quickly turned into one of my favourite Pokemon from any of the games... And that's proven by the amount of times I have trained Hariyama since.
Fire Red came along sometime around here... I tried to fix my past mistakes and decided to use Venusaur to see what it was like. Turns out, it was pretty damned good. Didn't have any issues with Misty (Wartortle gained dark typed Bite, so he was good here too). The team ended up being pretty different to my original team, but Hitmonlee made another appearance.
2007: Diamond
I got my copy of Diamond first out of my friends because I made a deal with a teacher who was going to America to buy it for me. Problem is... Diamond was horrible as a game. I was so excited about Sinnoh as a region, but it fell down. When Platinum came, it was a breathe of fresh air, and what the game should of been the first time around.
The other two slots here. Well, there were made up of Uxie and Dialga, because nothing else took my fancy in Sinnoh really. Also I kinda needed them because of the stupid level jump between Lucian and Cynthia at the E4. Pearl I ended up playing through a few times... but I never beat the Elite 4 again. The gap between Volkner and Aaron (and the rest of the Elite 4) was just too much.
When I came back later on for Platinum, I made a team which I much preferred and found the game a lot more enjoyable.
Unfortunately... This team had a horrible unseen Fighting/Fire weakness, and the match with Cyrus in the Distortion World nearly ended me. His Gyarados was very threatening after my team had been battered and bashed even getting to him.
Heart Gold was the game everyone was waiting for. I decided to trade over a few eggs to start off with. That allowed me to have a little choice in what I had but wanted to stay within the confines of what was available.
So I ended up with a cool team involving a Skarmory/Miltank/Donphan and ended up with a really defensive team which I really enjoyed playinbg. The other three were no brainers really for an ingame team for Johto. I did a great number of Silver playthroughs and covered a huge range of Pokemon. Some surprises inlcluded Plusle, Weezing and Chatot who were very effective.
2011: Black
When Black finally arrived over here, I was pretty stoked with some of the new Pokemon's designs (compared to a lot of other people). Gigalith and Galvantula instantly grabbed my attention and were dead certs for my team when they arrived.
Archeops became MVP with Acrobatics destroying most of the Elite 4 on his own. That thing has some scary scary power! Cofagrigus became a susprisingly solid choice too especially after it got Shadow Ball.
I've played White a huge number of times. Covered almost everything you can think of. Not having to use HM's during the story made a big difference in what became viable and the Pokemon choices you could make. My favourite team was probably the following:
A purpose built Sandstorm team that took on and beat Ghetsis at his own game. Omastar was tanking Hydreigon like he was made for it.
2012: Black 2
With the huge gap that came between this games Japanese release and it getting released over here, I had already pre-planned this team out weeks before the games dropped. And I (surprisingly) enjoyed it for the most part.
Sunflora and Azumarill were big shocks because they were actually pretty good! Dunsparce on the other hand was not... He was by far the weakest member of this team and I didn't overly like using him. I did however manage to keep him on the team for the entire game. White 2 I did not play as many times, I found it a lot more boring even with challenge mode applied... The level gaps were huge and all over the place, you practically lived off Audino. I did however make a dodgy sun team, but Ninetales is abysmally bad.
2013: X
X turned out to be a lot better than I expected. I held true to the fact that I should only use gen 6 mons for the first play through (as I had tried to do with other games).
Two not fully evolved mons! Didn't matter as XY was pretty easy anyway, and Vivi wrecked most of the game with help from Greninja and Talonflame regardless. No Megas for me until my second playthrough of Y where I used Mega Blastoise (and was pretty disapointed).
Ive got some other teams Ive used in Y too... One has just concluded but I really hated the team and it nearly stopped me form playing all together...
Anyway, that's my brief history of my teams and stuff that I've used. If you want to see more check out this imgur gallery of some of the other trainer cards I've made to show different teams: http://imgur.com/a/Vw4U6
Instead of putting down everything, I'm going to put in my "original" teams for each game and then highlight some of my favourite teams I have used. It's going to be a long one because I've got to try and remember all those years back to make up some of the teams I used.
1999: Red
Oh man was I a Noob back then. Pretty sure my first team was something along the lines of:






Blastoise was an will always be one of my favourite Pokemon. He saved me more times than I can count during the game. All the others are pretty self explanatory really. My brother used Vaporeon, so by default almost I went with Jolteon (and my small affinity for the Electric Type). Articuno replaced Pidgeot as my bird of choice, Zapdos also was in this slot too. Omastar and Snorlax rounded out the team with a strong Water and an amazing Normal type.
2001: Gold
Gold is what got me really hooked on Pokemon. Day Night cycles and different Pokemon at different times of the day felt like an appropriate and logical step for Pokemon to make. I made a bit of a booboo here as my brother had used Bulbasaur in Blue, and I thought I'd give the grass type a try this time around... How wrong I was.






Pretty solid team all round... Apart from me failing at Jasmine and having trouble with Chuck. I didn't understand Steel at all until Quagsire came to the rescue with Surf... This team was actually pretty strong in the end... Meganium actually started to hold itself up.
2003: Sapphire
Into 3rd gen and I was understanding how to construct and use balanced teams. This is way before I started doing runs for the sake of playing the game. But I found some excellent Pokemon in Hoenn.






Pretty standard RS team I think. Swampert for obligatory Starter and every other mon is pretty much have to use for a first RS game. Hariyama quickly turned into one of my favourite Pokemon from any of the games... And that's proven by the amount of times I have trained Hariyama since.
Fire Red came along sometime around here... I tried to fix my past mistakes and decided to use Venusaur to see what it was like. Turns out, it was pretty damned good. Didn't have any issues with Misty (Wartortle gained dark typed Bite, so he was good here too). The team ended up being pretty different to my original team, but Hitmonlee made another appearance.

2007: Diamond
I got my copy of Diamond first out of my friends because I made a deal with a teacher who was going to America to buy it for me. Problem is... Diamond was horrible as a game. I was so excited about Sinnoh as a region, but it fell down. When Platinum came, it was a breathe of fresh air, and what the game should of been the first time around.




The other two slots here. Well, there were made up of Uxie and Dialga, because nothing else took my fancy in Sinnoh really. Also I kinda needed them because of the stupid level jump between Lucian and Cynthia at the E4. Pearl I ended up playing through a few times... but I never beat the Elite 4 again. The gap between Volkner and Aaron (and the rest of the Elite 4) was just too much.
When I came back later on for Platinum, I made a team which I much preferred and found the game a lot more enjoyable.

Unfortunately... This team had a horrible unseen Fighting/Fire weakness, and the match with Cyrus in the Distortion World nearly ended me. His Gyarados was very threatening after my team had been battered and bashed even getting to him.
Heart Gold was the game everyone was waiting for. I decided to trade over a few eggs to start off with. That allowed me to have a little choice in what I had but wanted to stay within the confines of what was available.

So I ended up with a cool team involving a Skarmory/Miltank/Donphan and ended up with a really defensive team which I really enjoyed playinbg. The other three were no brainers really for an ingame team for Johto. I did a great number of Silver playthroughs and covered a huge range of Pokemon. Some surprises inlcluded Plusle, Weezing and Chatot who were very effective.
2011: Black
When Black finally arrived over here, I was pretty stoked with some of the new Pokemon's designs (compared to a lot of other people). Gigalith and Galvantula instantly grabbed my attention and were dead certs for my team when they arrived.

Archeops became MVP with Acrobatics destroying most of the Elite 4 on his own. That thing has some scary scary power! Cofagrigus became a susprisingly solid choice too especially after it got Shadow Ball.
I've played White a huge number of times. Covered almost everything you can think of. Not having to use HM's during the story made a big difference in what became viable and the Pokemon choices you could make. My favourite team was probably the following:

A purpose built Sandstorm team that took on and beat Ghetsis at his own game. Omastar was tanking Hydreigon like he was made for it.
2012: Black 2
With the huge gap that came between this games Japanese release and it getting released over here, I had already pre-planned this team out weeks before the games dropped. And I (surprisingly) enjoyed it for the most part.






Sunflora and Azumarill were big shocks because they were actually pretty good! Dunsparce on the other hand was not... He was by far the weakest member of this team and I didn't overly like using him. I did however manage to keep him on the team for the entire game. White 2 I did not play as many times, I found it a lot more boring even with challenge mode applied... The level gaps were huge and all over the place, you practically lived off Audino. I did however make a dodgy sun team, but Ninetales is abysmally bad.
2013: X
X turned out to be a lot better than I expected. I held true to the fact that I should only use gen 6 mons for the first play through (as I had tried to do with other games).






Two not fully evolved mons! Didn't matter as XY was pretty easy anyway, and Vivi wrecked most of the game with help from Greninja and Talonflame regardless. No Megas for me until my second playthrough of Y where I used Mega Blastoise (and was pretty disapointed).
Ive got some other teams Ive used in Y too... One has just concluded but I really hated the team and it nearly stopped me form playing all together...
Anyway, that's my brief history of my teams and stuff that I've used. If you want to see more check out this imgur gallery of some of the other trainer cards I've made to show different teams: http://imgur.com/a/Vw4U6