If you want a game that represents classic Mario annoyance, frustration, and difficulty but still modern, I highly recommend Super Mario Sunshine. However, like classy said, it's not easy getting all 120 Shine Sprites in that game. Especially the infamous Yoshi one. Or if you want a game with more story and substance than just rescue the Princess, play any of the RPG Marios, especially The Thousand Year Door or Bowser's Inside Story.

Or... if you want to get technical about it... there's always the Super Smash Bros. series.