The Goodbody Family was one of the many prominent families that lived in the Shire. The Goodbodies were connected to the Baggins Family through Bilbo Baggins's great aunt Lily, who married one Togo Goodbody. They were also connected to the Bolger Family; Cora Goodbody married Rudolph Bolger.
Among the family trees in Appendix C to The Lord of the Rings, their descendants are summed up in just two words: 'Various Goodbodies'. Bilbo acknowledged the connection at his famous Farewell Party: we know that at least some of the various Goodbodies were present at that feast.