Battle City is Namco's 1985 tank game, and the template for every top-down tank game since. You defend an eagle at the bottom of the map from twenty enemy tanks per stage, using brick walls you can shoot through, steel walls you can't, water you can't cross and bushes you can hide in.
Its lasting appeal is the terrain: the map is a puzzle you modify. Shooting a channel through brick creates a firing lane; leaving it intact protects your eagle. Two players can play together, which is how most people remember it.
Twenty per stage. Destroy them all to advance; letting them destroy your eagle ends the game immediately regardless of how many you've killed.
Yes — it was designed for co-op, with two tanks defending the same eagle on one keyboard.
Yes — a tiny 2D game that runs with nothing to install.