The Nintendo Wii has been out for well over a year now and I finally bought one a few weeks ago. I can honestly say that i can't think of anyone who wouldn't find the nintendo Wii fun. it appeals to literally everyone, from toddlers, to teenagers, to adults to your grandparents.
The Nintendo Wii is certainly not as appealing as the Xbox 360 or the PS3 when it comes to hardcore gamers. Most of them would prefer playing halo 3, Call of Duty or Gears of War, but what makes the Wii so great is that its much funner to play with other people, which certainly makes it a choice for parents who want to spend time with thier kids as a family.
the Wii has many exclusive games out now and coming out soon including Super Mario Galaxy, Super Smash Bros Brawl, Zelda: Twighlight Princess and Wii Sports. Games like Wii Sports really take advantage of the Wii's unique controller hat allows more movement and waving than any other controller.
The lack of third party titles for the Wii is it's only weakness. Many game companys tend to stay away from creating games for the Wii due to the unique controller. But the price is much more reasonable than that of the xbox 360 or Playstation 3 and the games are much more family friendly.