If I had to just pick one...hmm, that's a tough call, since there's really no Disney song I dislike, at least from the older stuff (which I consider anything Lion King or earlier and is what I'm most familiar with).
So I'll narrow it down to five...
5. Heigh-Ho from Snow White. My grandmother got me the Heigh-Ho Disney Sing Along Tape the day it was released. I was only a year old at the time, and this was probably the first Disney song I ever heard. It was a special moment for Grandma, as well--she saw Snow White in 1937 in the theater and wanted to share a childhood experience in this tape. (She later bought me the full-length film when it was released on VHS; last year we surprised her with the Blu-Ray). Snow White will always be special to me not only because it's a great movie and Disney's first, but because of Grandma, who's in declining health now but still wants to get back to Disney World in time for the new Fantasyland expansion.
4. Zip-A-Dee-Doo-Dah from Song of the South (which Disney needs to re-release sometime). It's a shame James Baskett died young, because I would have loved to have heard more of his singing (and given what I've read about their working relationship, I'm sure Walt would have invited him back for more movies). There are a bunch of re-recordings of this song, but for me, it has to be James Baskett singing it. Even though I'm too young to have seen SOTS in the theater (it was last released the year I was born), I was fortunate enough to have seen the sequence from this movie over and over on the Disney Sing Along Songs tape.
3. Let's Go Fly a Kite from Mary Poppins. Julie Andrews and Dick Van **** are great singers, but David Tomlinson is awesome too, and this song features his voice nicely. (There's also, of course, a bit of Dick Van **** in here, which just adds to the greatness of this song). I also love the literal interpretation of what one of my teachers called "the meanest idiom in the book". (She did mention Mary Poppins when describing this one!)
2. You've Got a Friend In Me from Toy Story (1, 2, and 3). Toy Story is one of my all time favorite movies, Disney or non-Disney, and when I saw the opening credits to this one in 1995 the song immediately got stuck in my head. The Spanish version from TS3 was good too!
1. When You Wish Upon a Star from Pinocchio. I know this is a boring choice for number one, but it's always been a song that perks me up even on the worst of days. However, I have a requirement--it NEEDS to be Cliff Edwards singing it, not one of these later re-recordings (I know Disney alone has re-done this one a million times with other singers since 1940). I do like the Glenn Miller version, and there's a pretty nice recording by Andy Williams on one of his later Christmas albums, but Cliff Edwards is the best.