Is there a way to deprecate a group? I have some groups that are part of an app

Group Administrators can delete groups from the people tab. Search for the group and then in the Details tab you'll see the delete option.

How might this affect running instances? Previouisly completed instances?

Well....if you have components that still rely on them, then negatively :-)

If you are using any of the groups to make assignments, control the visibility of tempo posts, define instance security, or access to documents etc.. then I wouldn't delete them.

If this just a case of the business not wanting to "see" them, in say the groupPIcker fields, on forms you could try using the "groupFilter" parameter to limit the list of visible groups?