Looking back, I've found that most of the times I died in past games were from "cheap shots" like the Meridia boss in Super Metroid (he's either really, really easy with an obscure trick, or amazingly difficult), or weird platform scrolly things and oddly timed jumps (like all of the automatic scroll levels in mario 3/SMW). So on one hand, I die less in newer games, but the games are also built so that I can avoid dying much easier -- retreating is easier, the puzzles are a bit more forgiving life-wise despite being more complex.
I also think a lot of the easiness comes from a well-fleshed out 3d world, too. Your options for dodging are pretty slim in 2d, whereas in 3d you have a lot more ways to avoid damage -- if you're good. If you try to just blast away at Ridley in Metroid Prime, you're gonna go down fast. Luckily the game builds you up to a level of skill where you figure out how to avoid attacks while delivering the most damage, which, personally, I think makes a game a lot more immersive.
So I don't think the games are exactly easier -- the developers have just gotten better at making good gamers