There's not much I haven't frozen. There are things that are recommended to not be frozen (like avocados), but we did it anyway. I would not recommend freezing cooked chicken by itself... didn't go over too well here. But, made in a casserole worked great.
I too used ice cube trays and then transfered the cubes to zipper freezer bags. For whole things (when finger foods started) I would line a cookie sheet with wax paper and lay the cooked veggies/fruit on them and then freeze.