Some forums got a "Thank you" feature, where if you like someone's post, you can just click on the link or button and your name gets added to the list of people thanking for that post. I would like that more than a voting system, feels more personal, and doesn't merge disagreements with agreements.
People would still post "+1" stuff all the time because they'd want their opinions to be more visible.
There's actually a solution for that (Facebook already does it). When someone "like's" something, it would show their name right under that person's signature on that post. "The following people appreciated this post".