Okay, reading this article about the MCU's lousy villains is making me realize that outside of some Batman villains, I don't really know any other DC villains either.  Chip's idea of a team-up is making me imagine Iron Man fighting the Joker, or Bane vs Captain America, or Two-Face vs Hulk, or Superman fighting Loki, or Batman Vs Ultron... those kinds of pairing seem interesting to me.