It's tricky to accomplish, but I believe you don't have to attack police in (at least) GTA 1 and 2. Maybe 3, but perhaps a mission requires it. Vice City I'm half remembering that you may have to actively annoy them to progress. San Andreas at the very least has a military-annoying mission where you'd attract too much attention to do a Terminator 2 and escape without killing. (Beyond that, I don't know how flexible they left it.)
It doesn't mean that police/military won't shoot at you, of course, but choosing your fights was always originally part of the risk/reward system (before the 'storyline' approach might have tied your hands). And there were joys to be had in evading the Harrier-like plane's missiles by flying the full-winged Dodo (with the advantage of being too slow to be intercepted, ironically, given that this is one of the real Harrier's tricks) until you can ditch from it and clean your record, after only provoking the forces of law an order by trespass to get the chase started. (Like forcing the train you hijack, and run backwards for a long run-up, 'through' the track-barrier that you're not yet supposed to pass, over into the other 'forbidden' territories, close enough to the military range that you can pinch the Harrier too, if you're quick enough. I think.)
But it's been a while. Thanks for the nostalgia, though.