Is there a way to erase an existing background to a photo that you took and create a new one?

Say there’s the normal picture of you taken at a bar or club or your living room and you wish to get rid of the background and insert your own.

I know you can insert icons over the background and you can frame your picture, but I want to completely delete the background and put something of my own.

Is there a program that can let you do this?