I literally just beat this game for the first time a few days ago. My brother and I used to play it on my grandpa's NES every time we would go there between moves (My dad was in the military, so we moved every few years), but we never beat it. World 8 was always too hard for our young selves to accomplish (We usually skipped all the other worlds with the Magic Flutes).
I downloaded it a few years back on my Wii for a little bit of nostalgia, but never put too much effort into actually beating the game. I brought my Wii out of it's box for the first time in years to play some Smash Bros. again when we decided to beat the game once and for all. We went through all eight Worlds without flutes or Paratroopa Wings. Feels good man.
It gets much harder than a lot of the recent Mario games. And although there've been some really great ones, Super Mario Bros. 3 is still my favorite Mario game. (Although that might change once I get my Wii U in a few days)