You guys got me interested in looking more into the palms and banana trees. Hubby wants the full tropical look out by our Indiana pool.

I was wondering how vigorous the root systems to these plants are since I have an above ground pool with a vinyl liner. I've decided against any type of bamboo for fear of some of their aggressive habits, but would like to consider some tropical plants that might endure our winters here.

Not sure about banana trees, but palms as a general rule do not have invasive roots.

Bananas in general aren't invasive , especially in Indiana . With that said I would not plant too close (4-5' away to be on the safe side) to the pool due to the fact that they clump and the clump will expand over time unless you remove some of the pups around the edge . Here is a link to a greenhouse in Indiana that specializes in bananas and tropical looking plants ...

http://northerntropics.mybisi.com/

Here in Portugal we have TONS of problems with palm roots invading drainage systems. We also have the palm weevil that has recently arrived in imported large palms from Egypt and it is destroying all palms but especially Phoenix Caneriensis. You're left with just the trunk after the weevils eat away the heart. For this reason I'm interested in fake palm fronds to decorate these stumps.
If you hear of anyone trying to import palms from North Africa or Europe you need to make them and the authorities aware of this danger.
http://www.naturalgarve.com/gardencenters_doencas.php
http://www.redpalmweevil.com/newlook/RP ... tugal.html