My DBF's little brother was about 2 or so when we went for the first time, and he had a blast. We did a lot of the character stuff with him (he was a little shy to the fur characters at first, but warmed up fast. And he was a ham for the Princesses.) We also took him on a lot of the rides he was big enough for. He wasn't so much a fan of Alice in Wonderland because of the loud noises, but he was alright with Peter Pan after the initial dark period. He didn't like the fireworks, again because of the noise, but we worked hard to get a spot by the rails for World of Color and he absolutely adored it. Needless to say, we took him in as an Elmo-nut and he left a total Disney-head. No more mention of Sesame Street once the mouse was in his mind.
There are plenty of things that kids that age will have a blast with, so long as you work well to stay in their comfort zones. If they don't like the dark, try to stay clear of Alice in Wonderland, Peter Pan's Flight, and the like. The rides at Bugs Land, the outdoor Fantasyland rides, IASW, and the Jungle Cruise were all winners. (We haven't been on The Little Mermaid Ride, but it doesn't look like the traditional dark-ride a la Alice;
youtube videos make it look much brighter with less to surprise, so it should be okay.)
If loud noises aren't their thing, again stay away from Alice in Wonderland. Peter Pan should be alright on noise. The fireworks can be upsetting, but we've learned our lesson and we're bringing some noise-reducing headphones this time. As for World of Color, it's an utterly fantastic show that everyone in our group loved, but for kids that small you really have to plan ahead. It's standing only for that show, which means unless you get right up by the rail a lot of it is blocked for the younger ones. Claiming your spot an hour ahead of time should get you a spot fine.
(Also, just a note...Nemo's subs seem very tame, but there is a *very* scary section with the Angler fish. The jellyfish also riled up DBF's brother badly, and he didn't like being stuck in that little dark sub. The memory of his tears on that ride are very vivid...he was pretty much shot for the rest of the day. So that's just something extra to consider.)
I hope that helps some! I'm sure you'll have some magical experiences on your trip!
You guys have NO IDEA how glad I am to hear all these success stories! DH has never been to DL and I havne't been in 15 years and am dying to go back! My friend and I always joke that when the kids enjoy the carwash they are ready for DL. Well both my kids beg to go wash the car so I guess it's time!! 
Now on to the planning!
