Personally I don't like the 4e 'Saving throw' as it was taking a term which meant one thing and made it into a 'duration determination'.
For 5e I'd prefer to see saving throws return as something your character does to avoid a nasty effect, rather than the 4e passive defences and attacks vs defences for everything.
In my ideal vision of 5e (yeah, right!) there would be 6 saves - one for each ability. You might make a Dex save against a fireball, a Con save against poison, a Str save against web, a Wis save against illusion and so forth.
I wouldn't have 'save or die', but I'd have the mechanism I first saw late in 3.5 of 'save or suffer a bad effect and make an additional save or it gets worse' etc. Thus if you get hit by a petrification effect, try to save. Fail the first save and you are slowed and save again next round. Fail the second save and you are paralysed and save again the next round. Fail the third save and you are turned to stone. Making a save at any point allows you to shake off the effect at that point. It also gives the dramatic potential for mitigating action to be taken before reaching the final state - whether it is quaffing a potion, allies taking actions to help you make a save, useful spells being cast and so forth.
Cheers