Definately checkpoints and infinite continues for me
Back in the old console and retro computer days you could more or less complete a game in a 2-3 hours. There were the odd few that included game saves like mario and desert strike, but they were few and far between.
These days games are more challanging and a lot longer in some cases, so not haveing the option would be a nightmare. Just imagine playing a game for 30+ hours and when you switched off you had to start again. Of course you wouldnt sit there for 30 hours straight unless slightly mad, so the saves would come in then too.
I do however like the idea of hardcore modes/challanges where you get one life and if you ide it's game over. Most recent example is the one in D3. Great fun
You still save throughout so you dont have to sit there for 20+ hours trying to do it.
So yeah, checkpoint's and saves for me
tris