For me, the first one that comes to mind is Bubsy. I don't remember any sort of life meter or anything that allows you take a second or third hit, like a mushroom in Mario or a ring in Sonic. You get running fast and suddenly a gumball machine kills you. Of course there is invincibility but short that, you can't take multiple hits.

Lolo is another one like this where it's instant death if an enemy touches you.

And of course all the old classics have that formula- Pac-Man, Galaga, Dig Dug, etc.