Slaver: Join Metzger's guild in the Den.

Separated: Have your spouse killed or sold into slavery, or get divorced in New Reno.

Prizefighter: Win the boxing title in New Reno.

Porn Star: If you shoot a movie at the Golden Globes.

Married: Marry Miria or Davin in Modoc.

Grave Digger: Dig up a grave other than Anna's, the fallout shelter in Golgotha, or the buried ghoul in Golgotha.

(For a woman, this should actually read 'Gigole'.)

Gigolo: Have sex a lot (or just once, providing you're extremely good at it).

Childkiller: Kill a child for any reason, even by accident.

Champion: Kill significantly more bad people than good people and don't be a Childkiller.

Berserker: Kill significantly more good people than bad people.

They don't affect your stats (other than Prizefighter, which could just as well have been a special perk), only how people in the game world react to you. They're often called 'karmic traits', or even 'perks', but the manual calls them 'special reputations'. During the game you will accumulate characteristics which are neither perks nor traits, but presented alongside them.

Fallout 2 the den quests