Finch is a member of an Earth gang called the Tenth Street Reds, which used to include a younger Shepard if the Commander has the Earthborn background.
Mass Effect
Commander Shepard can meet Finch outside Chora's Den in the Citadel Wards. Finch addresses Shepard in passing and identifies himself as part of Shepard's former gang. Finch says that another gang member, Curt Weisman, has been arrested by the turians for a "minor offence", though he is in turian space at the time. Finch asks Shepard to talk to the turian guard in Chora's Den to secure Weisman's release. He threatens to reveal Shepard's shady past with the Reds if the Commander refuses.
If Shepard decides not to have Weisman freed, Finch declares that he will inform the galaxy how Shepard was once affiliated with the Reds. Shepard can either convince him to stay quiet or merely shoot him. This choice affects the turian guard's opinion of the first human Spectre.
Mass Effect 2
Finch sends Shepard an e-mail if the Spectre didn't kill him in 2183. Although aware of Shepard's discontent at Finch finding the Commander two years prior, he encourages Shepard for working against the Collectors.