From Streets of Rage 3, throwing an enemy into one of the Bottomless Pits in Stage 3. You just lose a large amount of health if you fall into a pit. Enemies on the other hand, die instantly no matter how much health they had remaining.
The climatic battle in 3, against a hovering robot and racing against the clock to beat it. Given the higher default difficulty for non-Japanese versions, you WILL feel awesome when you get the good ending (by beating the boss before time runs out).
The Fan Remake
The Fan Remake deserves mention here, as much effort has been put into it, and it is generally praised as a worthy successor. Even Sega gave it a subtle thumbs-up, seeing as how they issued the cease-and-desist order only after allowing the remake to circulate around the Internet for some time.