Some versions of the Black Family Tree show the Weasleys are very distantly related to Sirius, and Harry's parents are part of that family tree.
Harry and Ginny are married at the end of the final book.
As Ginny is a pure-blood and James was a pure-blood, it is probable that they are distantly related in some form. There has been speculation as to who Harry's paternal grandparents were and it is possible that they were Dorea Black and Charlus Potter (however they may be distant relatives of the Potters). If this is true, Harry and Ginny would be 3rd cousins.