Is it possible to have great and a great relationship?

I really hope to have a long-lasting relationship someday with a person who understands me and I understand him. There's just one problem, it doesn't seem as though it will ever happen. I can't seem to meet somebody I connect with mentally and physically - I either get one or the other. I realize that no relationship is perfect but I want to meet that imperfect person who is perfect for me. I'm 24 and it seems like it's taking forever, I would like to be married by the time I'm 27 but it doesn't seem like it's going to happen. My question is: Is it possible to meet someone who is compatible with me both physically and mentally?