Backwards compatibility is fairly important to me, at least in terms of nostalgic value and convenience. I do like to revisit old games every now and then, but I can just as easily do so on their respective consoles, since Nintendo constructs their products pretty solidly, they tend to last a while in their own right. Backwards compatibility isn't a deal breaker for me, but it can become important for certain settings. For example, I don't have a DS and my two GBA's are on their last leg, so I was a tad disappointed when we found out that the 3DS won't be backwards compatible with that gen. (No biggie, I'm still buying it, of course) But now I know to expect having to pay some more money for a new GBA when my current ones die. Or, for example, I just moved into my dorm and was going to bring my Wii because of the backwards compatibility-- Obviously, that would mean a bigger library to play, including games that I'm in the middle of. That was a big reason that I was considering taking it, but changed my mind last minute to bring a gamecube instead; I feel like people would be more inclined to steal a Wii over a gamecube..
Anyways, I think it's a really nice feature to have, I like to take full advantage of it when it's included on systems