No, no guy is worth ruining a friendship.
I have a crush on this guy who dated my friend and I think he likes me back. Should I not date/like him because my friend did?
I would first admit that you have a crush on him to your friend, and depending on how she reacts it depends. Like she might encourage it, or she might seem glum
Ooh, this is a tough one. Some friends like to enforce the friendship code that essentially states "thou shall not court a previous lover of one of thou's friends" or, in other words, don't date your friends' exes. But other friends could really care less.
If you want to know for sure, then ask your friend about it and say that you and her ex are interested in each other. If you are too nervous or think it's too awkward to ask, then just assume that she does enforce this friendship code and don't date him. It's better to be safe than sorry.
Although ethics wise, it's probably not best to date him, whether your friend doesn't mind or not. I don't really know how to describe it, but it'd be awkward for your friend, that guy and your whole group of friends have had a history together since he dated one of you before, and there will always be some comparison between this relationship and the one with the friend either looming in the back of your head or the guy's head. It'd be difficult to essentially start anew. Plus it can be seen as rude to some people to do that, even if your friend doesn't mind.
So it's up to you to call the shots. I don't want to make any decisions for you because 1) I don't know your whole situation, 2) I don't want to risk messing up your life, it's your job to do that :P , and 3) this is an ethical dilemma and it's good to have some practice in dealing with it because there will be more to come. I wish you luck.