That becomes a trademark issue, rather than patents as this site is about.
But in essence, the idea of a trademark is to protect consumers from potential confusion. Speaking in somewhat abstract terms, you might a high-end restaurant that begins using McDonald's Golden Arches logo as their own. You can imagine a consumer driving by, seeing that logo, thinking it was McDonald's, eating, being charged $40 for a single meal, and never wanting to eat at McDonald's again, never knowing that they hadn't actually been to a McDonald's. Similarly, if I started sowing shirts and selling them with a NIKE Swoosh on them, consumers would likely be confused to find that a NIKE-branded article of clothing was falling apart with every touch. In many cases, trademark violations are bad for both parties.
So ultimately, that's what you have to look at. Will your "like" button be misleading to consumers? There are certainly a number of companies out there (including TIVO) that use a thumbs-up as an icon for "I like this," and it's a tough trademark to register due to its innate cultural relevance, so you can almost definitely get away with it. Just make sure it doesn't try to imitate the Facebook version and you should be fine.
I'm not actually 100% certain whether Facebook holds a registered Trademark on the "like" button, but regardless, you should probably still try to differentiate it just as a branding strategy, if nothing else.