Teenage Mutant Ninja Turtles Tabletop RPG Recommendations

Are you tired of the same old medieval fantasy RPGs? Do you want to role play a mutant animal character (possibly a turtle, or possibly something else)?  Do you want to use your ninja training to fight a criminal organization in an urban cityscape?

If so, this page has the RPGs for you!  We'll take a look at the official "Teenage Mutant Ninja Turtles and Other Strangeness" RPG (from Palladium Books, way back in 1985), and we'll also consider some more recent, generic RPG options.  These other options might not come with official TMNT franchise material, but they make up for it with much stronger rules than the official TMNT RPG.