Since hip hop is eligible and we got the big two inducted already (Grandmaster Flash and the Furious Five and Run DMC), my vote goes to "other" for The Beastie Boys (King Adrock, MCA, Mike D., and Mix Master Mike).
Their in the same vein as Run DMC in that with their original release of "License to Ill" they helped blow up hip hop in the late 80s (the album was also the first rap LP to top the Billboard 200 chart). They raised their game with "Paul's Boutique" which took sampling (courtesy of the Dust Brothers) to an insane standard that hasn't been reached since. Those two albums are essentials for early rap music.
Each subsequent album had a different sound and feel to it, with each also being a big seller. "Check Ya Head" had a mix of rock and punk, "Ill Communication" saw some jazz and funk, "To The Five Boroughs" was classic hip hop, and "The Mix-Up" was straight instrumental. Their versatility in music, impact on hip hop, and lyrics earn them a spot in my mind. Also, let's not forget about their activism with The Tibetan Freedom Concert in 1996, and just last summer the "Get Out and Vote" tour (which I attended twice in Youngstown and Dayton).
They didn't make the cut two years ago, but I'm hoping now that Run DMC are in they'll get another shot at it.
Speaking of the Rock Hall, when I was at the ceremony earlier this year the Mayor said the plan was to bring it to Cleveland every 3 years, so, who's eligible in 2012?