Personally I think it's important. I never owned an original Xbox but can find tons of games for it from $5-$20. The Xbox 360 is much more appealing knowing I could quickly build a library for it. I gotta think backwards compatibility has helped the Wii sell since it's library is still a little soft. Being able to augment with titles like Wind Waker, Metroid Prime, and Mario Party has helped it keep its momentum going.
In the case of the PS3, backwards compatibility may be hurting it. Since the PS2 was the last generation leader by a wide margin it's in Sony's best interests to kill it off. The PS3 needs more exclusive titles to succeed, as long as publishers are still supporting the PS2 that will be challenging. If everyone owns a PS2 it's not exactly a selling point for the PS3 to backwards compatible. I believe this is why Nintendo killed-off the NES as quickly as they could once the SNES was out.
<shameless plug>A few months ago a wrote on article on history of backwards compatibility:
http://huguesjohnson.com/features/backwards/ </shameless plug> - I talked about how backwards compatibility may be hurting the PS3 there too.