Here are some off of the top of my head. There's probably a definitive list out there.
  1. Minecart level
  2. Ice level
  3. Egyptian level
  4. Underwater level
  5. Forced scrolling level - a race to escape from rising water, lava, or the deadly edge of the screen
  6. Inconsistent water - on one level you can swim, another you drown
  7. The healing power of offscreen - enemies can regenerate if you leave an area then return
  8. The dead end the end of which you can't see until it's too late - in R-Type style shooters this is a classic
  9. Weapons disappear after 3 uses
  10. The Dark World / The Light World
  11. Food heals injuries
  12. Mimic Chests - regardless of the game universe
  13. Deadly Animals - even Spiderman gets his ass kicked by bees, rats, etc. in games...
  14. Train level
  15. Red Key for Red Door
  16. Incredibly useful power, skill, spell or weapon you can only use once
  17. King kidnapped and replaced by demon imposter - one for the Square fans
  18. Guns less powerful than bare hands - see Darkstalkers, Cadillacs & Dinosaurs, in fact most Capcom games!

(n.b. regarding NSA's excellent appraisal of Half-Life below : I would say that the game does feature a couple more of the cliches listed, just in slightly disguised forms : there's the occasional headcrab in a crate that serves the purpose of a "mimic chest", and I could've sworn there was something akin to a minecart level about halfway in).