In a romantic context, a person could feel that another person "belongs with" him/her (e.g., "You belong with me, forever and ever"). However, only a slave can "belong to" another person. Otherwise, see smrkrbb's examples above.

'Belong to' describes ownership: the blue 1963 Ford Thunderbird belongs to me, the rusty 1989 Dodge belongs to you. It's the traditional sense of 'belong'. 'Belong with' describes similarity and where something should be categorised: in a library Dickens belongs with Hardy and Austen. You can also use 'belong' with other prepositions as well: 'Your Dodge belongs on the scrap heap, Dickens belongs in 19th century, etc.

belong to someone: this house belongs to my uncle. belong to something: i used to belong to a youth club.

I'm sure you know how "belong to" works; as to "with", that kind of means "have things to do", "(equally) own each other (therefore belonging to each other)".