That depends greatly on what you're talking about.
Since I'm far more comfortable with an airbrush than a paintbrush, I generally paint small parts own their own, then assemble. Like so:
If it's something that'll need seam repair - a fuselage, wings, wheel halves, etc - then I build first, then clean up, then paint.
If it's something that will be extremely difficult to mask later, I'll paint it first, too. The red cowl ring on P-47s of the 56th FG, for example.
The thing, IMO, is to figure out what works for you. I read an FSM article last fall where the author stated he prefers to paint all the stowage, tools, etc after they've been attached to the tank. To me, that's a giant NO EFFIN WAY!
On the Bench: 1/32 Trumpeter P-47 | 1/32 Hasegawa Bf 109G | 1/144 Eduard MiG-21MF x2
On Deck: 1/350 HMS Dreadnought
Blog/Completed Builds: doogsmodels.com