Victoria & Albert's is the only "dressy" restaurant. Here men are required to wear a jacket and most men do wear a tie. The women dress nicely as well.
The finer restaurants outside the theme parks (CG, Narcoosee's, Citrico's, Artist's Point, etc.) do not have a real dress code but do usually say no tee-shirts. People tend to "clean up" a bit but are still casual. Depending on the occasion (business, special event, etc.) some people may be dressed up a bit and others will be in nice shorts or clean jeans.
Any restaurant in a theme park, even table service, is pretty much "anything goes".