This is growing in the cattle pens. It's not a rampant vine. Probably only grows somewhere from 6-9'. It grows from a tuber or bulb and is perennial, dying back to the ground in the fall and then returning in the spring. The leaves are very thick and waxy - very succulent like - especially when the rainfall is good. The blooms are inconspicuous, but make clumps of berries for seeds. It climbs by attaching with tendrils and the stem doesn't twine. Doesn't seem to be a host for insects, but I expect it is spread by birds dropping berries/seeds. I find it an attractive foliage plant and have considered trying it as a climbing vine in a potted plant situation, so if anyone recognizes the plant and knows about any negative aspects, I'd appreciate the information.

Overall look of the vine:


A bloom - sorta:


The berry clusters after bloom:


Tendrils:

Try looking up cissus trifoliata.

I think you nailed it Greene! How'd you know that? I've searched Google for photos of native Texas vines and couldn't turn it up! No negatives either, so I can safely try it, but one common name was 'cow itch' :). Apparently it grows a bit longer than I've ever seen it grow here. Probably a response to more rainfall than we see. Thanks Again!

In answer to your question of 'how'd you know that'...I didn't. No clue. But I was wondering if the vine would make a good houseplant.

I use key words like 'Texas Vine' in Google Images and look for the shape of the leaves. This is good excercise for my old eyes and helps me to better observe details.
When I find a photo similar to yours I click on the links, such as:
http://www.catnapin.com/WildFl... and
http://www.delange.org/GrapeIv...

I quickly read the details. If I have the wrong plant, I start over.
If I think I have the correct plant, I plug the botanical name from the link into Google Images and search again, looking for more details.

When I was a kid I thought that reading the encyclopedia was a fun pastime. The computer is my new encyclopedia; it helps that I don't have an active social life and have time to do this kind of thing.
Good luck with the plant.