The Animated Music Video to Disturbed's "Land of Confusion" cover features a (possible) Zakk Wylde look-alike, amongst others. Could be a reference to the original video, which featured multiple celebrity puppets. There's also the Sniper on the back of the album it's from, Ten Thousand Fists.
The classic 1962 novelty hit "The Monster Mash" was performed by Bobby Pickett in an obvious Boris Karloff imitation. Subverted when Boris Karloff himself performed it in the 1965 Halloween episode of "Shindig!" That particular performance was lost; a recreation was posted on YouTube.
Jon Lajoie's WTF Collective 1 and 2 have this. MC Fatigue is Sean Paul, MC Final Verse is 50 Cent, MC Confusing is probably Lil Wayne, MC Inappropriate Rhymes is probably Kanye West, and the Chorus Guy is supposed to represent how rap songs will have some random non-rapper sing the chorus.
Beatallica (a satirical band performing mashups of The Beatles and Metallica) already has a singer who does a dead-on James Hetfield... and they fall straight on this in "And I'm Evil", featuring a GlennDanzig soundalike. ("Am I Evil" was not by one of Danzig's bands, but...)
Pet Shop Boys alluded to the controversy of the time about Eminem's homophobic lyrics with "The Night I Fell In Love", by writing a song in which a young gay man has an affair with a closeted hip-hop star who has pretty clear parallels to him. (Eminem responded by doing a video in which he ran the Pet Shop Boys over with a car. Stay classy, Eminem!)
Pulp had numerous celebrity impersonators in the video for "Bad Cover Version" in a parody of We Are the World/Do They Know It's Christmas-style charity videos. The impersonators range from Liam Gallagher, Robbie Williams, Rod Stewart and Tom Jones among a dozen others.