I still like Tom and Jerry, it's indeed a classic series. I always root for Tom, since I like cats a lot. He is also more likable than Jerry. Tom is funnier and his constant failures to catch the mouse (Or mice, since there is also a grey one) awaken pity in the viewer. The mouse on the other hand is boring, always escapes in the end and has a presence of arrogance that makes Jerry clearly the real evil one of the pair.
I also disagree with everyone who said that you can be too old to enjoy watching it. If you still like to watch Tom and Jerry, go for it. Abondoning things just because of that reason instead of really stopping to like it is just trying too hard to be a cool adult.
"Look how cool I am, I am denying the greatness of all things that I liked as child, because I am now a cool grown up who realised that life is serious business."