If the environment is busy, then the autopilot probably goes in after 500' (but before 1000') just to keep the workload sensible for the other guy. London, New York, etc.
If it's less busy, then I like to fly the departure using normally LNAV/FD, or until vectors put us on a straight line, or we get held at an intermediate level for a while. Preferably up to 10000'. I include it in my brief normally.
I do know some people who chuck the autopilot in as soon as possible, irrespective. I haven't managed to get bored of flying yet.