Völgarr The Viking, Shovel Knight and Odallus come to mind. SK has checkpoints, but I think they're only halfway-through a level. Dunno about the other two.
VVVVVV was fun as well, as the only one of these I've actually played. Usually a single checkpoint halfway through a stage. There's a true ending you can only get by beating the entire game on one life.
One more that I just scrolled past on Steam: 1001 Spikes. "1001 Lives to pass 100+ Levels" Interesting spin on this, I think.
Volgarr the Viking is hardcore as fuck. You died? BACK TO THE FUCKING START SHIT SUCKER.
When I got to the second level it was a god damn accomplishment.
spoiler (click to show/hide)
This is probably why I also have barely played the game.
Dying in Shovel Knight was a little less of a punishment but it still made it feel like having lives mattered. The game also doesn't hand lives out like candy on Halloween like most recent Nintendo platformers. I *will* say that NSMBU was pretty fucking hard at times and actually made lives feel like they mattered, because the game only lets you save after beating the mini castles or end castles. I haven't played 3D World yet but if its like 3D land then lives are probably of little consequence.
The first DK game on Wii was also pretty hard and running out of lives sucked. Tropical Freeze seemed to add more checkpoints so it wasn't as awful.
These days I find gaming discussions weird. Easier than ever to find something that strikes your fancy, people still stuck on forums whining about shit.
I admit I mostly only like talking about games with other people who make games, because the discussions can actually get interesting and go beyond blind fanboyism. Not always though.