Desert - sand
And that's it. I sat and thought about it for a bit, and yeah, deserts are actually the only biome I consider absolutely essential. Some other biomes I get excited when I see them, though:
Extreme Hills - I love these for the views and for building on :) Good for mining, too, since emeralds spawn here, and I don't know, mines just seem to fit in with mountains.
Jungle - cocoa beans, parrots, ocelots (less important now that we have stray cats)
Dark Forest - I love me some dark oak wood :)
This isn't what you're asking, but the biomes I don't really like to see are:
Savannah - ugh. Ugly.
Plains - ugh. Boring.