Well, usually I just punch its lights out with a CC to the face on any of my "regular" teams.
However, on my mono-special teams, I usually have a few ways to get rid of her:
Stat up and attack: Let's face it, a Blissey does not like a +2 Focus Blast coming from the likes of Infernape. The only problem is Blissey never switches into those sort of pokemon, but she does switch into Slowking, who can easily stat up on her and kill her with +6 Surfs (provided it isn't a Toxic or CM Blissey).
Stat up and Baton Pass: Much like the last one, but I have something that can set up on Blissey, such as Celebi, get some boosts in then BP them to something that will ruin Blissey's day.
Toxic: Used more to screw over CM Blissey, force switches, and kill Blissey if it's the opponent's last pokemon. I usually use Blissey for this, since she can switch into status and isn't afraid of the opposing Blissey's attacks.
Taunt: Basically, I taunt it and keep attacking while it cannot heal itself or use status. I've only had this work with Houndoom, though.
Destiny Bond and Perish Song: Pretty self explanatory. The former works pretty well but I can't screw up the prediction at all. They both can help take down CM Blissey.