Here's some ideas for digging out some of the larger ones.
http://www.freeplants.com/tree-stump...structions.htm
If you have lots of them you might want to consider purchasing one of these. If memory serves me, the forestry service uses them.
http://www.misterhoneysuckle.com/
For any that you can't dig out you could cut flush to the ground and use this organic method to help the stump and roots to decompose.* If you have a pruning saw that would work on the smaller trunks.
http://www.dirtdoctor.com/view_question.php?id=50
Newt
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.