Oops. Yeah, I'm kinda tired right now. You can draw 5 watts, if you run it at the default 5 volts.
National semiconductor does say the LM 7805 can supply over 1 amp, but they don't say how much more. Fairchild says their equivalent chip, the MC 7805, can supply up to 1 Amp. Probably 1.5 amps is its highest limit.
You are right Sebi, the 7805 has thermal overload protection. I guess you could use it at 1.5 amps, with a large heat sink. Panji, you could also use the LM 350, which provides 3 Amps of current.