I have to somewhat agree with Aolish's theory: younger gamers are generally going to prefer the newer games, or at least the games that they first played. I've seen this on other boards with regard to The Legend of Zelda and Final Fantasy series (many OoT and FFVII fans).
As for myself, it's no surprise that my first Phantasy Star game is still my favorite: Phantasy Star I. I got it on Christmas Day of 1988 (along with the Sega Master System). My first RPG experience, it was obviously unlike any other game I had ever played before. I remember telling my mom, "Hey, you don't die in this game!" That was because I hadn't left Camineet yet.
I played Phantasy Star I for quite a few years but somehow never got Myau to fly up to Lassic's castle in the sky (even though I had the Laerma Nut). Anyway, I loved exploring the three different planets, especially using the Ice Digger in Dezoris! I still remember the two towns on the planet where everyone called the people in the other town liars.

Although I no longer have a Sega Master System (or Genesis), I picked up Phantasy Star Collection on GBA (my first purchase for the system), so I can try and beat the game, once and for all (I've been busy with a lot of other games).
What I love most about Phantasy Star I is the music. There are so many great and hummable themes in the game: the title screen, Palma, Motavia, the dungeons, etc. Sometimes I'll turn the game on and leave the title screen on just to hear the music for a few minutes. I also love the exploration. I played the game before the Web and online maps, so like many other kids, I had to draw my own maps. One of my best memories was getting lost in Maharu. I had to find Noah twice and then find my way out - that actually took a couple of months. I still remember finding all of the Laconian weapons, and fighting the different-colored dragons. I would say that Phantasy Star I is one of my top five favorite games of all-time.
My second favorite Phantasy Star game is Phantasy Star II. I got it in 1990. I'll admit that I used the guide throughout the game (I even brought it to school and read it during class, lol). Similar to my experience with Phantasy Star I, I got up to Dark Force but always lost. Like Phantasy Star I, II has a lot of great music. The "save" music and Paseo town music are both excellent. I hope that if I have enough free time this spring and summer, I can finally beat this game.
Right now, I just recelty downloaded Phantasy Star IV. Is it an awesome game or what!? While the music isn't as good as in I and II (although there's an area that seems to be the Biosystems Lab from II and music from a dungeon in I) the game moves along rather quickly, which is certainly a change of pace. I like that I don't have to level-grind too much (although I do prefer getting the best items for my characters before going on to the next mission). Even though I'm only four hours into it, I can see why many other fans like IV so much. Lastly, I know there are vehicles in this game, and I can't wait to get them!