Cosmic Encounter

You control an alien race trying to establish colonies on other players' planets. Every turn involves asking others to ally with you in attack or defense. The constantly shifting alliances and ridiculous alien powers cause great moments. The setup takes a few minutes, but it is worth the effort once you get going. Players stay engaged even when it is not their turn because the board state changes constantly. It scales well whether you have a full table or just a couple of people. I like how it forces you to adapt your plans on the fly. You might get frustrated if your initial strategy falls apart, but that is part of the charm. It sits on my shelf as a consistent backup plan for rainy afternoons.