RE1: Its almost impossible for me to try to even aspire for "objectivity" in judging this game: its one of those games I will love and defend to unreasonable lengths no matter what. I know that its technically lacking in most regards when compared with later games, but I still love it. Its like that wonderful B-horror movie you love to watch time and again with your friends and then make up jokes and puns about. The legendarily hilarious dialogue is masterful in its subtlety (basically: you can't make this stuff on purpose if you consciously tried to aim for "bad voice acting"!). Everything about the game, the characters, the mood, the setting of a deserted mansion in the middle of the dark woods, I love all of it! And yes, the soundtrack of the first, non-dual shock version is definitely the better one, I think it stands head and shoulders over every other RE soundtrack. Basically, a great game hampered by some cumbersome controls and somewhat slow pacing, but with so much personality that I find myself returning to it over and over again.
RE2: Another classic, and probably the best oldschool RE if you're going by "objective" criteria. What I like best about RE2 is how ingeniously designed and thought-out it is with the branching paths taken by the two characters and the ways in which the story progresses. The whole story flows fluidly from location to location and makes the player suspend a whole boat-load of disbelief (a huge mansion-like police-station stuffed with works of art and secret passages? an underground laboratory complex hundreds of meters below a city? suuuuure...). Its not my favourite in the series, but there's on the other hand really nothing negative I can say about it, either. A fun oldschool survival horror ride.
RE3: Disliked this one intensely when it first came out, but like it somewhat better now, even though its still the weakest of the original PS1 trilogy. Like Amazingu pointed out, the "scares" are much cheaper, and it feels more like an action-game in a horror setting. It feels like the series definitely "went Hollywood" in this installment with explosions, monsters around every corner, and an invincible freak constantly chasing you. The gameplay feels a bit smoother and more streamlined in RE3, but in other respects, it just feels like a step down from RE2 and its definitely lacking RE1's atmosphere.
Code Veronica: Liked it a lot when it came out, but I've never found myself returning to it, and the end result of the experience felt pretty bland and forgettable. The soundtrack is good, but the characters and scenarios are just either tedious and completely uninteresting (Steve and his damn adolescent whining all the time), or completely incredulous and just over-the-top (the part of the plot stolen directly from Psycho, flying a fighter-jet to Antarctica, etc.).
RE1 Remake and RE0: I should have liked these more than I did, but by this point I just felt fatigued by the series. The Capcom-syndrome struck again: the games weren't bad by a long-shot, but were so similar to their predecessors that I just lost the passion for them. REmake is the better of the two oldschool GC games, it relies on the original RE1's great atmosphere and setting and really only needs to clean up some stuff and re-do the graphics (which are lovely!). The new additions were pretty meh, but I could live with them. RE0 was really more of the same in every single way minus the feeling of nostalgia REmake could boast, and it didn't stick with me, it was one of those games I enjoyed playing through but quickly forgot and never returned to. By this time, the time was way overdue for a re-vitalization of the series, and RE4 really delivered here!