In my case, I'd say that the Wii has indeed lived up to my expectations!
I'm not really a gamer. I only bought the Wii for our family (and also friends who visit) to enjoy. In fact, if not for the Wii then we wouldn't have any games console at all. If I would've bought an XBox or Playstation, only our eldest son (7) and maybe myself would use it. The simple reason is that most people (who aren't into video games) can be bothered to sit down and fiddle with controller pads for hours on end.
So far, the family (myself included) has had lots of fun with the Wii and it's definitely a big attraction when friends come to visit (even more so when we have parties). The games are short and the control mechanism is easy to understand (what could be easier than swinging your arms?). This means anyone can play and you can quickly take turns.
Sure, the Wii can't compete with the XBox 360 or PS3 in terms of raw processing power but it's obviously not meant to. The Wii was designed to appeal to a broader market. Of course, Nintendo needs to address the needs of the true gamers and I believe they will. Firstly though, I think they need to capture this wider target group.
Considering the fact that I (and I guess others like me) have bought a Wii and that I'm happy with it, I'd say Nintendo has succeeded.