The only real difference between an inverting op amp and a non-inverting op amp is the "inverting" part.. otherwise, they both have the same applications, essentially.
Most common use is simply as an amplifier, for:
- stereos
- sensors (photo, temperature, pressure.. anything)
- repeaters (ie. signals lose power when transmitted.. and if transmitting over long distances, need to boost the signal)
Another use in a lab I did was as a noise regulator (wrong term.. but that's how I'll describe it). Ever notice how some tv shows are much quieter than the LOUD commercials? By using op amps (and some more circuitry), you can essentially set a maximum volume level.. I forgot how it works, but I believe it utilizes the range where an op amp no longer amplifies..