Saving Private Ryan is an excellent film, but I don't really think of war scenes as "gun fights," mainly because when I watch a gun fight in a movie, it's to be entertained by absurdity, not shocked by the reality of what people actually went through. You can't watch Saving Private Ryan's Normandy scene and scream "FUCK YEAH" unless you're a legitimate psychopath. It's a heart-wrenching display of the horrors of war. So while it's well done, it's also a scene I'm not itching to watch over and over.
John Woo needs more representation in this thread. Hard Boiled may be the best pure gun fight movie of all time, The Killer has some excellent gun fight scenes, Face/Off has some excellent gun fight scenes (particularly in the apartment), A Better Tomorrow has some excellent gun fights in it... The dude knows how to film a shootout. Step 1: Akimbo pistols. Step 2: Slow-motion. Step 3: Motherfucking doves. Step 4: There is no Step 4, because literally anything else thrown into that mix would destroy your mind.
That said, here's my list:
3. Predator - Storming the rebel camp (great action, great one-liners: "I ain't got time to bleed," "stick around," etc.)
2. Hard Boiled - The hospital scene. Fucking A.
1. Heat - The bank job. A scene so insane they made it into a GTA mission.
Honorable mention - The Matrix lobby scene, which I've probably scene more than every other shootout in movie history combined. I've come to find it slightly overrated, but that's probably just boredom through repetition.