I'll admit it, I added that Mahna Mahna entry to TV Tropes.
I don't know off-hand how many times the song was done back in the 1970s, but early on he was used in other contexts a fair amount of times. He did the String Quartet sketch and Sax and Violence, and while they weren't really major parts for him I'd also like to provide special mention for his appearances as a Hawaiian in the Spike Milligan episode and as part of the "Short People" band in the James Coco episode.
Then he wasn't used for many years before being brought back to lip-synch to his famous song at Muppetfest, and since then there's been quite a few performances and parodies with Mahna Mahna. Many of his appearances in the Boom! comics work in some variation of the song. His name is not all he can say, though the one time he had a lot of speech isn't exactly something many casual fans have seen (I do kinda wish I could see the Snowhts talk normally).
And there's the fact that in Bip Bippadotta's last Sesame Street appearance he shouted "Mahna Mahna!" Most of his appearances had him speaking coherrently (and he looked considerably different in the Sesame Street version of the song). Though the two are considered different characters, casual fans probably don't know the difference (though Bip was used in more significant ways than Mahna was). Sometimes I wonder if even Sesame Workshop knows they are different characters, since all album versions of the song credit the singer as "Ma Nah Ma Nah", and sesamestreet.org has that name as a search result for his clips (though the Mahna Mahna song isn't included). It can be especially confusing since neither character is ever directly referred to by name on-screen (and the one time Bip's name was mentioned was in the album credits for Every Body's Record, which was the first appearance of "Everybody's Song", a few years before it was on the show, and from what I read the album doesn't have a gatefold with images... casual fans might not instantly know it's him). But then again, Sesame Workshop must be aware of the different characters, otherwise they wouldn't have put him in a 2009 episode.