Not very at all in some cases, very in others.
You see on one hand, I have only every put in one GameCube disc into my Wii just to see how it worked. It did. Wow. So I turned it off. I have yet to do it again.
On the other hand, I have the new PS3 slim that isn't backwards compatible. I was looking in a game sale deal bin and saw Shadow of the Colossus, a game I have always wanted to play. I was about to buy it and realized I couldn't play it. So, I unfortunately left it in said bin. *Sniff!*
So, when it comes to games I've already played, I don't particularly care. If a Wii 2 can play Wii 1 games, I really wouldn't care as I would still ahve my Wii available. I buy all Nintendo console systems and have since the orignial NES' original release, so it's no skin off my nose to remove that backwards feature.
When it comes to games I haven't played though, I would love it. I went from the original Game Boy to the DSi without playing any handheld Nintendo system in between. So, I've missed out on a LOT of great titles. I wanted the DSi for the prospect of a VC, but they didn't implement it. Because of this, I don't have GBA compatibility, so I'll have to hunt down used systems to catch up on old titles. I realize it's harder to do with cartridge based systems, but still, it would be nice. It's shame so many classics have gone off the radar. A VC would eliminate my need for backwards compatibility, or in Sony's case - a FLESHED OUT VC would be better. I like their offerings I can download to the PS3 Slim, but I need more especially when it comes to games like Shadow of the Colossus.
In the end - short answer - Important for systems I don't follow each iteration, Not Important for Nintendo Consoles!