For starters, keep your fragile stuff (wands, bottles) in a chest, so they won't explode on your face.
Changing the weapon class after UT2 is generally a bad idea.
A cloak of fire protection is extremely handy to have.
Don't save health potions until you're about to die, chances are you die before getting the liquid down your throat.
Pray to gods every 2.5-3 hours. If you do it more often, they get annoyed.
If you're having difficulties getting past Jenny (the huge plant on UT3), a wand of teleportation/polymorph is sometimes an easy way out.
I'd have a lot more tips, but you should see the Little Details topic instead. A lot of good info there. Also the wiki is available.
Welcome to the forums