Pyrotek - good for large orders, extensive inventory. It's what I usually use.
Discount Pyro - Small inventory, good prices.
United Nuclear - good for small orders, small inventory. No longer stocks KClO3 or KClO4.
Firefox-FX - good for large orders, extensive inventory
Skylighter - good for large orders, extensive inventory
Cannonfuse - fuse and tubes only
Iowa Pyro Supply - medium-large inventory, looks good.
Dawntreader - medium inventory, prices look good.
Pyrohobby.com - Small inventory, kinda expensive, no ID required.
Pyrostuff.com - Teeny Tiny inventory, kinda expensive.
ClayArtCenter.com - Potassium nitrate and a couple other chems used in pottery.
Rocketry.org supplier list
Stanford Systems Aerospace - The shitiest supplier ever. Ordered from there, has taken 5 months already, no sign of my chems yet, slow to no email response. Do not order from them!
For information on ways to obtain chemicals locally, go to the Local Supply page.