For something offbeat… I find Flight of the Conchords, a “folk parody” duo from New Zealand with their own HBO show and an album, to be hilarious.
For example, their rap song “The Hiphopopotamus vs. Rhymenoceros” is a classic. (See also the TV version, which is considerably modified.) For more great rap, listen to “Mutha Uckers.” (“I pay my mutha uckin rent fortnightly…”)
Then there’s “Frodo, Don’t Wear The Ring.” (The video is even funnier in the context of the show.)
Their great love song is “Business Time.”
If sci-fi is your genre, check out “The Humans Are Dead” (and TV version). Binary solo!
There are other funny ones, but those are some of the ones that continue to crack me up.