As mentioned, Mission: Space is a definite no-no for folks who are claustrophobic.
Also, something like Star Tours *could* feel claustrophobic for some people, because you're in an enclosed space, but it's big enough to seat about 40 people, so it's not tiny like the 4-seater Mission: Space capsules. I'd say the ST cabin is about the size of my bedroom, and I don't think my bedroom is that small.
Also, perhaps avoid the tunnels on Tom Sawyer Island. They can get a bit tight for an adult.
Being restrained in your seat in the darkness on Stitch's Great Escape could be a bit much for some claustrophobia sufferers...
But one that didn't really occur to me was Soarin', until I rode with a friend for her first time. At the start of the ride just before lift-off, the front of the "wing" above you tilts down a couple of feet. (The reason for it while on the ride is to block your view of either the feet of the people above you if you're in rows 2 or 3, or the top of the screen if you're in row 1)
My friend got a little apprehensive from that wing lowering. But that was just for those few seconds on the ground, when your view is very restricted. Once up in the air, you have a very large field of vision in front of and below you and don't feel closed in at all. (That's where a fear of heights would start to play in...)
-Rob