You know, the kind of song that feels as though it's two different ones wrapped into each other, or one that starts off as one thing and ends up something drastically different. It doesn't have to be rock either, any genre is fine.

I don't really know of any you don't probably already know of, but when you mention that, I instantly think of War Pigs. (technically it is two songs but still)

Err, I'm not sure if this counts but a lot of System of a Down songs have really heavy parts followed by melodic ones ala Bohemian Rhapsody (Sugar and Chop Suey come to mind)

Looking for more than just an intro... hmm... try 'Saffron's Curse' by Cradle of Filth, or anything at all by Rhapsody. Harpischords ahoy!

November Rain by Guns n Roses certainly has two parts to it, as does The Crab Song by Faith No More.

Most Yes songs are made up of more than one song, and they put out singles for the main part of the song. Starship Trooper and All Good People come to mind.

Meat Loaf and I would do anything for love. Mmmmmm meat loaf.
Red hot chilli peppers ,Under the bridge .

If you're wanting more tunes that sound similar to Radiohead's work, check out a band called Muse.

Webpage

Strawberry Fields and A Day in the Life by the Beatles. To a certain extent, Stairway to Heaven

well, i know one: Jesus of Suburbia by Greenday, and some others by CO&CA i know you wouldnt like, so i wont post them.