We have a 5 month old and he's been on Kilamanjaro Safari at AK, at Mk he's been on Snow White, Buzz Lightyear, transit authority and POTC, at Epcot he's been on Living with the land boat ride, spaceship earth, universe of energy, imagination, and the Mexico boat ride.
You can take your baby on any ride w/o a height restriction. We took our baby twins (at 7 mos. old and at 13 mos. old) on almost everything in Fantasy Land in MK, along with the rides mentioned in the above post. We used those baby bjorn front carriers on the rides as it made our babies feel secure and we didn't have to worry about them being jolted around at all.
Let's see, my son was 1 when we went last year and he rode .. the carosuel, Dumbo, Magic Carpets, Pooh, Small World, Transit Authority, Kilimanjaro Safari, the train. I am sure there were more, but I can't think right now!!!
My babies really loved the Spectromagic parade, winnie the pooh ride, and its a small world, if its open when you go. They didn't get much out of the safari, because the animals were too far away for them to see easily. Also, the Lion King show at AK for all the music and clapping.
Also- if its warm, its really fun to put a bathing suit on a todller and let them run around in the jumping fountains at Epcot or downtown disney. (I guess thats not exactly a ride, but its fun! Strangers stopped to take pictures of our kids)
and she went on so many rides. I'm not a big roller-coaster person, so she probably went on just about any ride I went on! There is so much for the little ones to enjoy. Don't worry...you won't be looking around trying to find stuff to do!
We took my DD on Dumbo, Pooh's Honeypots, Cinderella's Carousel, the Tea Cups, Tomorrowland Transit Authority, It's A Small World (but it isn't open until next spring) and the Riverboat.