Here are some off of the top of my head. There's probably a definitive list out there.
- Minecart level
- Ice level
- Egyptian level
- Underwater level
- Forced scrolling level - a race to escape from rising water, lava, or the deadly edge of the screen
- Inconsistent water - on one level you can swim, another you drown
- The healing power of offscreen - enemies can regenerate if you leave an area then return
- 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
- Weapons disappear after 3 uses
- The Dark World / The Light World
- Food heals injuries
- Mimic Chests - regardless of the game universe
- Deadly Animals - even Spiderman gets his ass kicked by bees, rats, etc. in games...
- Train level
- Red Key for Red Door
- Incredibly useful power, skill, spell or weapon you can only use once
- King kidnapped and replaced by demon imposter - one for the Square fans
- 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).