If you feel pity, you feel sympathy for someone else's suffering. A documentary on prisoners who have been wrongfully convicted might make you feel pity for them.
Use pity as a noun or a verb. You feel pity for the really bad singer so you try to look attentive, but then you pity yourself for having to suffer through his terrible rendition of "Somewhere Over the Rainbow." We also say something is a pity if it's something to be sad about. It's a pity that your computer crashed right after you finished your paper.