This article is from the of the muppets FAQ, by Craig Silverstein with numerous contributions by others.
These have definitive answers, from the performers.
Clifford is a human: In the Billy Crystal episode, Clifford says to Rizzo, "I'm the man and you're the rat. I've got genetic seniority." In early press releases for "Muppets Tonight!" he was referred to as "Clifford the Rasta," but that's his religious affiliation, not his species. In the Garth Brooks episode, Kermit calls Clifford "catfish-faced" but never actually calls him a catfish. Which is good, because he isn't one.
Pepe is a Prawn. (From _Muppets From Space_: "I am a King Prawn!")
Eugene, Nigel the Director's buddy -- the one who pops out of the control panel during the opening sequence -- is a mink. This isn't actually a Frequently Asked Question (to date, it's been asked all of once) but we threw it in because of its trivia value: Steve Whitmire contributed this answer during discussions of "Muppet Classic Theater" (in which the mink's head-banging performance in "Gotta Get That Name" stole the show for many of us). This was the first ever post of a Muppet performer to alt.tv.muppets, the progenitor of rec.arts.henson+muppets.