Humblejoe, it all depends on your tastes.
Alien versus Predator can be really scary. you've seen Alien 1 and 2 yes?
Play a marine! Do it in nighttime

And be careful to watch your beeper heh..heh.heh..
If you want to go for a jolly-fest gogo run, go for Serious Sam. It's silly, but got huge monsters and battles. It's like go back to the good old Doom2 days.
I'm playing Quake3, it's free once you got it, lot's of free servers out there, and it got exciting physics. Made by the great progreammer in the industry John Carmack. But Quake 3 is a sociable sport, so it's quite something different again. But I'm having loads of fun with it, both in tricking and ordinary play.
Deus Ex is a good old one too, it's a little too tweaky and you're too weak at the beginning, but it got one of the coolest stories and places, and you got much stealth mode. It's a futuristic Cyberpunk tale.
Theif 1 is a classic. It's THE thief game. And if you love the idea of hiding around, sneaking into mansions stealing a precious vase for hire etc.etc. this game was really exciting. Also got great levels and story!
Half Life is a all time classic. You're hard to find one guy not recommending this one. It's a basic Soldier run, but it's extremely well made for it's time.
Try to get Doom2, it's my old time fav.