I thought Tyrion was endearing, mainly from the standpoint of him being the only person trying to be decent amongst his purely evil family. He found himself fighting on the wrong side more often than not, and usually it was because he didn't see it until it was too late.
From just a TV show perspective, Dinklage absolutely hit it out of the park with his performance.
From a character standpoint, Tyrion had a pretty good redemption arc (even if he did commit patricide). He may not have been a good person (especially at the start), but he wasn't evil. He did try to be a good person (most of the time).
Plus he had a bunch of witty one-liners.