It matters a little bit how you define "die." I mean, if I lose a life playing Super Mario World, technically I've died, but I certainly haven't got a game over. Or if my main character dies in an RPG but the rest of my party's alive, does that mean I've died there as well?
Assuming you mean "Games you beat the first time through without getting a game over (or getting kicked back to the last save point, in games where you never technically get a game over)", I can pretty much say that this didn't happen at any time during the NES or SNES era, with the possible exception of Gemfire. I don't remember my first playthrough, except that I'm sure I picked the Blanche family, and probably the Gemfire scenario, which is pretty darn easy. So there's a reasonable chance I beat that game the first time I played.
Moving on to the PS1/2 era, I can't remember any titles in particular, but I know I played at least a few pretty easy RPGs in my time. In Final Fantasy IX, for instance, if you don't count taking the wrong path in an early cave and ending up on a plateau with a bunch of overpowered dragons on it (and then spending the next three hours or so figuring out how to kill said overpowered dragons, just to see what kind of crazy loot they'd give...not much, as it turned out), I think I might have played through that game without dying. Eiko's Pheonix ability is just that powerful, and coupled with the Chakra ability and a copious supply of pheonix downs, it means that an opponent has to be killing, on average, more than two party members each turn. That just never happened. It probably helps that I tend to rack a little more than strictly necessary in most RPGs I play.