Depends on what you're raising, broilers, (and what kind, Cornish X, Freedom ranger, Red broiler...) or heritage/dual purpose breeds, and time will vary with breed.
C. X, you can start processing any time after they get feathered out well, the small ones dress out nicely for Cornish Game hens you see at the store. I think that's at around 4 weeks. The supermarket birds are anywhere from 5-6 weeks old when processed, most home grown ones are kept to 8 weeks, 10 weeks for roasters. I have kept some longer, for even bigger roasters, but just like any other chicken, if you wait too long, you'll have a crock-pot bird. That's not a bad thing, I love crock-pot chicken, but you just need to know what to expect at what stage.
I haven't raised those for quite awhile, though I recently had some undersized birds left from a commercial grow out, that a friend gave me. Once I got them, they grew fast, most of them, I think they had just been the less aggressive ones and got pushed away from the feed.
Mostly I raise dual-purp, and usually I butcher at 20-25 weeks if I want a big, meaty bird. You can butcher sooner if you like, the older they are, the more they need long, slow, cooking at low temps. If you want a fryer or a broiler, you need to butcher them young. They won't be very big, but they'll be more tender, allowing for faster cooking.
If you're raising dual purp, read up on cooking methods for older birds, that'll give you a better idea when to butcher for what purpose.
Don't forget you need to let the meat rest in the fridge for at least 24 hours before freezing or cooking. This is useful for any bird, more so with older ones.
