Super Mario Bros 3 doesn't just hold up--it is arguably better than most modern games.
Cons: No saving in NES version; Bit of a difficulty spike late in the game
Note: This review is based off of the All-Stars version of SMB3. There isn't a whole lot different between the versions though, so most things said in this review should count.
NES games, being early in the history of video games, have several old design flaws. Mega Man and Punch-Out!! are unfairly hard; The Legend of Zelda is confusing; Metroid is both. And those the games that have held up best and are still fun to play today. Super Mario Bros 3 is one of the only NES games that doesn't have this issue. Super Mario Bros 3 was so ridiculously far ahead of its time that it trumps a lot of modern games, and is still a blast to play.
For all intents and purposes, Super Mario Bros 3 might as well be the first real sequel to Super Mario Bros. Unlike The Lost Levels, things are changed, and unlike Super Mario Bros 2, the core is UNCHANGED. The basics of the first game are in place-run and jump over obstacles to reach the end of the level-there's just a whole lot more of it.
It's amazing really, how much more content is in Super Mario Bros. 3 than was in either of its predecessors. The amount of power-ups has grown exponentially, with staples like the Raccoon Tail, or the Hammer Bros suit; there are roughly double the levels (although to be fair, they are pretty short) and they are accessed via world maps; not only is there more than one boss, but there are now nine, and the list of changes goes on.
And almost all of it is really well implemented. The level design really shines in Super Mario Bros 3, with a great variety of styles and themes (pipe mazes, moving floating platforms, ice levels, etc.). The sense of discovery from the first game is not only preserved, but greatly enhanced here as you never know what the next world will bring-the first time you see an airship is pretty amazing in itself, and it's nothing compared to the first time you enter Giant World. And the sense of discovery keeps going: there are so many replay-value increasing secrets-some even let you beat the game in under an hour.
It's not a perfect game-the difficulty spikes pretty high later on, and there's no saving in the NES original-but by and large Super Mario Bros 3 is really, really great. A lot of NES games I can recommend with the usual "old game, old flaws" warning, but that's not necessary with Super Mario Bros 3. Even if you ignore away the giant step forward in gaming history that Super Mario Bros 3 represents, you are left with an extremely fun game that doesn't show its age in the slightest.