It depends both on the model, and what you are painting "for."
Take a Space Marine - with the bolter leveled across his chest, the Eagle becomes almost impossible to paint. If the backpack is on, it's a pain in the neck to get transfers - or freehand details - on the shoulder pads. So I'll generally leave the guns and backpack off, paint those seperate, and then glue them on at the end.
Now look at a Black Templar - with their crazed arms-out-to-the-sides poses, you can get to just about everything after it's assembled. BUT - I find it's easier to leave the shoulder pads off so I can prime the body black, and the pads white.
Now - what are you painting for? If you're painting a gaming army, and want to get the models from blister to table as quickly as possible, then stick the whole thing together. If you can't get to it with a brush after that, you won't be able to see it from the tabletop anyway!
If you're painting for competition or display, however... I tend to leave much of it seperate, assembling at the end, ensuring that I can get my brush into every niggly detail.
So look at each model on a case-by-case basis, and come up with a plan of attack that best suits the model.