HearYouNow from ExSilent
ExSilent, a Dutch hearing aid manufacturer, developed this free app that lets you adjust for frequency and distance of sound, and lets you adjust your two ears separately, and instantly replay the last 20 seconds. Maybe it's because the company sells actual hearing aids, but ExSilent stresses that the app is for people who have trouble hearing in specific situations. If you're using it all the time, they write, you should probably see a doctor.
Hear from Loyalty Works, Inc.
This free hearing aid app is so basic, it's offered in the Entertainment category, with numerous disclaimers, including a warning that it "may damage hearing permanently." It doesn't appear to have any adjustment controls to speak of. (The banner in this screenshot, from the AppStore,