There are three dangers in tombs; Traps, Zombies, and Mummies. You don't need to worry about the last two if you're a vampire or necromancer (though they may counterstrike or curse you if you keep poking them).
Tombs have lots of stuff, and better quality than keeps. Spotting traps lets you train observer.
Traps are no big deal, usually. Get some intuition and observer at character creation and you'll be able to spot almost all of them.
Zombies are annoying/deadly. They can shatter your skull through your helm with a punch, but have terrible to-hit chances and are at 60% of unskilled peasant speed. Don't get surrounded. Don't let them charge you. Don't chop off hands or heads as the mummy will probably reanimate them. If you find a particularly trap-rich room, you can lure them over the traps. Basically, attack one, then back up, wait until it comes to you, then attack and back up again. As New Guy said, your best bet is to remove all the corpses from the tomb, but this takes time.
I am reasonably sure that the mummy only resurrects when you either come within one tile of his/her coffin or take something from the tomb (not sure if it's anything at all or just specific items). Uzu says traps also trigger awakenings. Mummies can only be killed by cutting off their head or cutting them in two (so, sword or axe)(soldier mummies will have helms and body armor, making it harder/impossible to kill them). They will raise all the corpses around them, again and again. They will also curse you, which never goes away and gives you a 20% chance to fail at any skill roll, which usually results in a quick and amusing death. The curse is for the 'disturber only' and is line of sight. Getting someone else to go near the coffin first might work for eating the curse. If your ambusher is good, you can sometimes stand next to them for several turns before they spot/curse you. Waking up the mummy and then running away far enough will make it disappear, this is a filthy exploit for cowards. Saving and reloading also seems to do this (even worse exploit).
So, what I do is to sneak all the time, explore the entire tomb and decide which items I want and find where the mummy is, then grab what I want and gtfo.