First and most important, I like combat to be the exception, not the rule. Serious combat should happen perhaps once a session; small skirmishes a bit more often, but preferrably not. When a person dies, I like there to be implications to that death, whether it be PC or NPC.
That being said, for the most part I like combat fast, furious, highly dangerous (this does
not map well in D20), over, and done with. Combat that lasts more than half an hour of real time to adjudicate just gets boring. Once in a while a longer combat can still be fun (ask my group about The Pirates On The Island, where we spent nearly half the six-hour session in running combat -- very tense night all around!), but that is a rare exception.
Combat should not be strictly, "I move, I hit". There should be some serious options for tumbling, scuffling, and other non-hitting activities in combat.
As for minis ... meh. I'll use them in D20 since the system more or less requires it, but it has never felt right. I don't like the "gods' eye view" of combat; having been involved in several SCA wars, paintball skirmishes, and some truly odd LARPS, I have come to realize how poorly such a system simulates how most combat works. People/targets appear and disappear, depending on landscape, helmets, weather, and the like; sounds seem to come from all over; split-second tactics are useful, but strategy flies right out the window for the guy on the ground; weird things come to your aid and hinderance all the time. And, believe me Critical Fumbles HAPPEN! Until you've seen a guy in the SCA coming at you with a great sword, and you know you are dead, dead, dead, and then suddenly a blackbird flies right in front of his helmet and he trips, you've never really dealt with fumbles...
So I prefer a bit of cinematic fun to the combat, a bit of reality, quick combat with some good options, fumbles to match critical hits, and less of an emphasis on the mechanics (and miniatures) and more of an emphasis on the roleplaying.
...of why I'm out of step with most of the rpg community...
