I'm fond of virtually all of them, for varying reasons. I love hard 2D platformers, and it's hard to get much more classic than old-school Castlevania. I will reserve special appreciation for IV, because of the variety packed in to it (I still think it's one of the showcase SNES titles), for the unusual but effective design choices especially in the music (largely quiet, atmospheric pieces rather than the more usual goth-rock, but it fits so incredibly well), and for historical purposes (Love games by Treasure? This is one. Their first big one, I think).
Perhaps the perfect expression of the Castlevania sidescroller, though, is Rondo of Blood (aka Dracula X Duo, NOT the SNES version). Play it on the Wii Virtual Console if you've never tried it. Warning though, Maria is hugely overpowered.
Metroidvanias are probably my favourite sort of game overall; my wife and I still play through Symphony of the Night on occasion. I've liked all the GBA and DS iterations (though I wasn't much impressed by Harmony of Dissonance), with a special like for Circle of the Moon and its massive series fanservice. Yes, I know it's an early GBA game and the visuals are rough if you're not playing on a big screen GBA Player, but really it's all about the music. Almost all the soundtrack of CotM is made up of remixes from old games, some rather obscure (even from the Genesis Bloodlines!).
And really, Castlevania is all about the music. There might not be any game series where the music is so consistently high-quality. Fans can name so many quality tunes that so often get remixed throughout the series: Vampire Killer, Bloody Tears, Beginning, Simon's Theme, Blood Relations, Wicked Child... Castlevania is perhaps the soundtrack perfection of classic videogames.
I can't call out a favourite. IV, III, Symphony, Rondo are all up there. There are few I don't really care for, though Harmony of Dissonance and Adventure I (the first GB game) are among the less impressive. I reserve judgment on 64, because I never got to play it with a proper working memory card. Was not impressed with the first PS2 game and haven't touched the 3D versions since, but that's not a Castlevania thing: I'm just a 2D gamer in general.