Very good question.
Personally, I'd recommend: sticking with D&D! It was the first fantasy role-playing game and despite the dozens I've played it's still one of my favorites. It's really hard to compare to the true "D&D" feel.
However, since most of the game designers are now dead/switched companies the latest versions of D&D seem to be losing their "D&D" feel, in my opinion. If this is your feeling as well, you might be looking for some new (good) systems to try out. This is pretty much what I did the hard way (by buying them all). Overall, I was mostly disappointed. I couldn't really find much to compare with 3e and 3.5 (not sure which system you use). Even basic D&D was pretty darn cool.
Okay, assuming you're still looking for a new RPG to try out, here's a rundown of some of the ones I've seen/heard of/owned/and played:
Pathfinder: Really, this is just D&D 3.75 under a different name. If you're a big fan of D&D this is a pretty cool game to get into. It's very complicated and rules heavy, but it still retains that 'true D&D' feel.
Horror Rules: This is a nifty little horror role-playing game I came across. I don't even like horror role-playing games, but this one is so hilarious and awesome I'd recommend it to anyone.
Apart from that, I don't really recommend the other major RPGs I've gone through. Here they are anyway:
GURPS: this game has a lot of cool powers. However, the 2d6 core mechanic is a little wonky. Also, it's power based so you're either an invincible, incorporeal monster, or a guy who can drive and shoot a gun (and will also probably die if you get shot).
Savage Worlds: Everyone seems to love this game. It's nice and simple, and works well. However it's a bit too 'normal' for me. One of my players got shot and died. We're kind of more used to heroic fantasy than miniatures combat. Savage Worlds has a strong tactical and miniatures edge and it functions universally allowing you to play sci-fi, or what have you.
Ars Magica: This game is highly role-playing orientated but the mechanics struck me as kind of odd and open to interpretation.
Mutants and Masterminds/Other d20 settings: these seem to be mostly a rip off of 3e and I wouldn't really recommend them. This goes for LOTR rpg and the WOW RPG as well.
Warhammer 40K RPG and Dark Heresy/Rogue Trader: these games seem to cater more to the miniatures fans of the games they represent. They don't strike me as so workable in an RPG. The d100 core mechanic is a little wonky, but semi-workable. You might enjoy them, but they're not really to my taste (I gave away my Rogue Trader book I bought for like 60 bucks without reading it more than once or twice).
Good luck on finding a great system!