I've run into this line of thought myself. Off the top of my head, you could try a lot of things. Heart and favorite are a couple that I haven't seen others in here use, but are still used in popular sites (Tumblr and Twitter).
There are so many of these sites that have similar messages, I think what you need to decide is what will your users best identify with? If you put too much pressure on being unique, you may just alienate people. I've seen others go as far as making up words for what is clearly a 'like' functionality and it didn't pan out too well.
If you want to avoid being associated specifically with Facebook (or g+ or whomever), you might consider just using a heart, a star, or a thumbs-up icon.