Honestly all the other answers are good but they are lacking the real counter: Celebi!
So it resists both its fighting STAB and grass STAB moves while hitting back hard with Psychic or sometimes the good old HP Fire that people use to hit Ferrothorns. Also Substitute takes care of Spore, and if you don't have it Natural Cure does the job.
Celebi @ Leftovers
Trait: Natural Cure
EV's: 252 HP / 216 Def / 36 Spe
Bold Nature (+Def, -Atk)
- Giga Drain
- Hidden Power [Fire] / Psychic
- Baton Pass / Calm Mind
That said Gliscor is also a great counter to Breloom. it resists its fighting STAB while its great Def means it can take Seed Bombs all day. Gliscor can also avoid Spore by using its own Toxic Heal. Ice Fang gets the job done easily enough.
Gliscor @ Toxic Orb
Trait: Poison Heal
EV's: 252 HP / 252 Def / 4 Atk
Impish Nature (+Def, -SpA)
- Ice Fang
Once you have poison up Spore is useless.
So I understand that the other answers were up way earlier, but I wanted to add this because these two are really good at countering Brelooms.