How about clematis? They won't harm a tree unless you use Sweet Autumn, which is too heavy I have been told.

What about Cardinal Climbers? Very light and very pretty. Attracts hummingbirds.

Clematis is an excellent choice!!!!

I have had the same question for awhile now! Thanks for posting everyone :)

peas and pole beans are fine as companion plants. They fix nitrogen in the soil which releases to the tree roots. Some sites list them as specific beneficial plants for fruit trees in general. Perhaps bush beans would have a similar effect. In any case, you not only get a fruit crop, but you also get peas or beans!

Nasturtiums work great