Strictly speaking, Breloom does not have a 100% standard counter, since Spore will almost always disable them as they switch in. The closest thing to a Breloom counter is Hypno, who resists Focus Punch, can OHKO with super effective STAB Psychic and is immune to Spore thanks to its Insomnia ability, though it must invest heavily in HP and Defense to avoid a 2HKO from Seed Bomb. Honchkrow also has Insomnia and can OHKO with STAB Drill Peck, but takes heavy damage from Focus Punch. Neither of these two are much use in standard play except for this purpose, however, so you should consider other viable checks to Breloom. Most of the time the easiest way to get rid of it is to let it sleep one of your Pokémon before going in for the kill, as Sleep Clause prevents it from trying the same trick twice.
Of bulky Pokémon, Celebi resists both of Breloom’s STABs, and has STAB Psychic or Hidden Power to destroy Breloom with. It is also faster, immune to Leech Seed, and has Natural Cure to get rid of sleep status. Cresselia can take a Seed Bomb or two and resists Focus Punch, so provided you have anything else to take the sleep it becomes a decent option. Weezing can take almost anything that Breloom throws at it barring Swords Dance Facade and hit back with STAB Sludge Bomb or Fire Blast. Roserade and Venusaur both resist both of Breloom’s STAB moves, and both can kill with STAB Sludge Bomb. Sleep Talk Rotom-A is immune to Focus Punch and can take a Spore, but if Sleep Talk selects the wrong move he is likely doomed, as Seed Bomb will usually 2HKO all but the most defensive variants.
Flying-types are particularly painful for Breloom to handle. Crobat and Yanmega both have quad resistances to both Breloom’s STAB moves, though Crobat does not have the crippling quad Stealth Rock weakness of Yanmega, while both can OHKO with Brave Bird or Air Slash respectively. Crobat can also use Taunt to avoid Spore and outruns even Scarf Jolly Breloom, but both hate Stone Edge. Gliscor makes a good check if it runs Aerial Ace, though Earthquake is not doing much to Breloom, and if it tries to Roost and is faster it will eat a super effective STAB Seed Bomb. Salamence and Gyarados both have Intimidate and Salamence resists both of Breloom’s STAB moves, however Gyarados is at risk from Seed Bomb, and both hate Stone Edge. Gyarados will also usually lose if it does not carry Ice Fang or Bounce, as Breloom resists all of Waterfall, Earthquake and Stone Edge. Similarly, Zapdos works well if it has Heat Wave or Hidden Power Ice, but may struggle if it lacks either of those, as Breloom resists Thunderbolt and Hidden Power Grass. Skarmory takes a heavy amount from Focus Punch but has STAB Drill Peck and Brave Bird and can Whirlwind away the SubSeeder.
Choice Band Scizor can revenge-kill weakened Breloom with Bullet Punch, or U-turn out to scout and break Breloom’s Substitute if it stays in. Sleep Talk Heracross resists both of Breloom’s STAB moves and can do serious damage with its own STAB moves, but needs to invest in HP to avoid a 2HKO from Stone Edge. Toxicroak resists everything Breloom commonly carries and can OHKO back with Poison Jab or Sludge Bomb. Lastly, Dugtrio usually carries Aerial Ace for the purpose of removing Breloom and Heracross, but cannot afford to switch in on any of Breloom’s moves.