Your actual karma level will be described using the karmic titles, from "most good" to "most evil": Savior of the Damned, Guardian of the Wastes, Shield of Hope, Defender, Wanderer, Betrayer, Sword of Despair, Scourge of the Wastes and Demon Spawn. Each 250 karma in either direction from 0 will earn you a new title. I find that being a shameless opportunist will net you a high positive karma in the end - which could mean that the designers have strange notions about morality, but more likely just reflects the fact that there are more good things to do in the game than bad ones.
Reputation in specific towns are reflected by the standings: Idolized, Liked, Accepted, Neutral, Antipathy, Hated and Vilified. Like your karma level this is a representation of a numeric value, only this one is hidden. You always start out as Neutral when you come to a place, except Klamath where you're Accepted if your CH is 6 or more, and Vault City where you start out with Antipathy. In Arroyo, of course, you're Idolized. Sadly it's not possible to reach Idolized in all settlements if that's your aim. At the Ghost Farm, for instance, you can't advance beyond Neutral even after saving all their sorry asses.
It should be noted that karma and reputations all have a much smaller general impact on the game than one might think. They make a difference in the case of critters that look directly for certain reputations or threshold values of karma or town reputation, but the basic reaction system that factors in everything at once is used very little and doesn't even work properly. It won't really make any difference whether you have 500 karma or 1500.