This thread will be riddled with the mistake that "emulator" means "ROM on computer, and illegal." When I'm playing a game emulated, it's usually on my DS. The Virtual Console is legal emulation.
That being said, my opinion is mixed. I'm all for paying Nintendo for their work, using the controller the game was made to use and all that. But on the other hand, I can play Super Mario All-Stars on my DS (SNEmulDS is a bit buggy at times, but when it is it's usually with battle backgrounds in EarthBound... and Tetris Attack, that's really difficult to play).
The moral value... I don't see anything horribly wrong with playing a game I already own anywhere I want. That, and I believe that if you can't currently buy it from Nintendo, it's not illegal. So, for now, stuff like Majora's Mask is fair game. And EarthBound... It's criminal of Nintendo to have not yet put it on the Virtual Console, at the very least.
As far as save states go, I only use them when I need to stop playing but can't actually save--I don't continue from states twice.