With access to one of the best moves in the game and an Attack stat that makes even Heracross jealous, Breloom is an underrated and excellent Fighting-type. Most notably, he packs resistances to both Earthquake and Rock Slide.
Breloom can be a pest for any team, even prepared ones. Thanks to his access to the perfectly accurate Spore, Breloom is an awesome sleep-inducer. The strategy is simple: switch Breloom in on either a predicted switch or into an Earthquake or Surf, use Spore, and then Focus Punch. Hidden Power Ghost will hit everything that Focus Punch doesn't, but Hidden Power Rock is more effective on Flying-types, such as Salamence. Snatch is a great move to use against opponents that attempt to use Substitute to block Spore, and it can grab Dragon Dance boosts from a weakened Gyarados or Salamence if your prediction is spot-on.
Breloom works especially well in tandem with Magneton, who baits out Blissey. There's no point in running a Jolly nature, as the additional Speed doesn't let him outrun anything significant. In particular, he will still falter against most Pokemon trying to outrun Jolly Tyranitar.
Don't discount Breloom's ability to use Substitute and Leech Seed; he will tear through many standard teams if played properly. Generally, you will want to bring him out against a Pokemon he outspeeds. As the vast majority of people will switch in a sleep absorber in fear of the imminent Spore, Substitute is usually the best move. Behind a Substitute, Breloom can annoy the hell out of its foes by restoring its HP with Leech Seed, dealing extraordinary damage with Focus Punch, or putting to sleep with Spore.
Spore should be saved until the opponent brings out their Breloom counter, but it might sometimes be necessary to use it earlier. This set forces so many switches that you will be in heaven with Focus Punch if you can predict well, and if you manage to get Spikes down on your opponent's side of the field, they will be taking tons of damage. Enjoy taking teams out with this surprisingly puissant Pokemon.
Swords Dance is great for getting a few boosts after a Spore. Charm is another extremely underrated move Breloom can learn, as it greatly cripples Salamence, the most common switch-in to Breloom. The Attack drop prevents Salamence from dealing the beastly amounts of damage he normally does, and supports your team.
Checks and Counters
Skarmory works decently; in addition to high Defense to wall Breloom, he also has STAB Drill Peck or Hidden Power Flying to KO Breloom. However, Skarmory doesn't take Focus Punch too lightly. In general, Pokemon that resist Fighting-type moves and pack a super effective attack work well; examples include Weezing, Salamence, Gyarados, Celebi, Venusaur, Moltres, Heracross, and Crobat, as well as Zapdos that carry Hidden Power Ice. All of these will be put to sleep by Spore, though, so either use Sleep Talk on them or have another Pokemon absorb the Spore. Dugtrio obviously can't switch in on a Fighting attack, but with prediction or by sacrificing something else, he can finish off a Substitute-less Breloom with Aerial Ace.
Insomnia Pokemon that are immune to or resist Fighting moves are also excellent checks: Banette can cripple Breloom with Will-O-Wisp, Hypno has access to STAB Psychic, and Ariados packs STAB Sludge Bomb. However, the former two should avoid Hidden Power Ghost, and the latter Hidden Power Rock.