I am no fanboy, but rather from a marketing profit standpoint, Nintendo as a company is pure genious.
I think they did it with price point and an appeal to simplicity. The PS3 and its counterpart are very specialized machines - they cost a lot. Moreover, they are somewhat complex because of the integration of all that other stuff like Blu-Ray, PS store, etc. (I'm mostly thinking PS3 here). In a word, it's for geeks (like me). The Wii doesn't appeal to geeks as readily as the others do. But the issue here is that the Wii also appeals to parents thanks to "games" like Wii Fit and the Sports one. These games are nothing spectacular to look at, but they retain their fun value for all the age groups.
Yes, marketing genius. Personally I don't like the Wii, and even with a price drop I won't buy one (again, geek factor!), but I agree that they made the Wii to be cheap and simple so it appeals to all age groups. The others didn't quite do that, in my estimation.