Given the sheer length of time Sesame Street has been turning out TV shows, it's not surprising that they have multiple alphabet songs in their repetoire. Here are 3 fun ones -- one very recent, one not too old, and one that if you remember it, you'll remember it from when you were a kid.
First up, the most traditional version from Tilly and the Wall. The first time I saw this was a couple years ago on the actual show, and it was so visually and aurally arresting that I stopped what I was doing and watched the whole thing. It's bright and colorful and percussive and... just... happy.
Tilly and the Wall (on Sesame Street) - "Alphabet Song" [Vimeo] (you can even download it at that link)
Old -- I have faint memories of watching this as a child. Much more relaxing than Tilly and the Wall's version.
Sesame Street - "Madrigal Alphabet" [YouTube]
This one's a little newer and according to the YouTube post, comes from a DVD, and perhaps not from the show itself. I had my doubts before I clicked "play" (Kermit and a Zulu tribe? Really?), but it works quite nicely.
Sesame Street - "African Alphabet" [YouTube]