Alright, since we're all doing lists, I'll do mine as well. I would like to make a quick note though, that (assuming you've played it), I think RE1 and REmake should both be included and have different placements on the list. They are completely different games, at least IMO, and both should have a place on any list. REmake really isn't a port or replacement for the original, at least to me.
Anyway, my rankings go like this...
1. RE4: the best of the action RE's, hands down. Incredibly well designed action game with a few moments of Horror here and there, and the best boss fights of the series. Terrible story though, albeit with fun and cheesy dialogue. Also the game that started it all with Mercenaries. Yes, RE3 has Mercs, but it's not really the same thing.
2. REmake: the best Survival Horror RE, hands down. Incredible level design, fun puzzles, cool enemy designs, Crimson Heads, Lisa Trevor, outstanding atmosphere, it's all just so good. The replay value is through the roof as well, with a dozen (!) endings, various weapons and costumes as unlockables, and a ton of different gameplay modes that actually feel like they had a lot of thought put into them, and are really fun as a result. Great game.
3. RE2: incredibly fun and well designed game, with some of my favorite monster design in Birkin. I love the A and B scenarios, and how different they are from one another. I will say that outside of the Police Station though, I find some of the other locations to be less memorable overall. I would prefer 3 to 2 honestly, if it weren't for one small thing...
4. RE3: I LOVE Nemesis, I love ammo crafting (it adds an almost RPG esque element where you choose the type of ammo you want to focus on) , and I love Raccoon City as a setting for the game. Mercs is also fun, albeit very different from later games. The main thing I hate about this game is the Dodge mechanic. Would it have been so difficult to put it on a button separate from the ones you use to aim and shoot!? I hate when I'm fighting fast aggressive enemies like dogs and Hunters, trying to shoot them, but Jill just keeps dodging and getting hit. Ugh, so frustrating.
RE1: REmake is better in many respects, but I still adore the original. It's still fun after all these years, and the voice acting is pure gold. Just brilliant Grade A cheese, as are the live action cutscenes. So hilarious, haha. One thing I will give it over REmake though, is the soundtrack. Seriously, I think it's the best OST of the series. It's eerie, atmospheric, foreboding, and occasionally very rock n' roll. So awesome and RE1's credits sequence is pretty much my favourite ever, as well. Love seeing all the highlights from the game with Still Dawn playing over it.
I'll place the rest in a different post.