The Nintendo Wii is the first video game console to successfully incorporate interactive game play, a character that defines it from competitors PlayStation 3 and XBOX360.
The introduction of the Nintendo Entertainment System secured the idea of every house having a gaming console; because before it, consoles like Atari were not fun to play and out of peoples' price range. Nintendo made consoles much cheaper, more fun to play and thus widely available to the world. Super Nintendo expanded on this, offering even more games, with better graphics along with the same reasonable price tag. RPGs reign supreme on this console; titles like Final Fantasy III, Chrono Trigger, and Breath of Fire are considered timeless masterpieces even today.
When the Nintendo 64 came out in 1996, PlayStation already had a year head start and was had secured many Sony loyalists. When someone was deciding between the two consoles, it came down to colorful graphics and shorter loading times (because of the cartridge) on the N64 side, or games with deeper storylines, longer game play, and more role playing and fighting classics like FFVII and Tekken on the PlayStation side. For most players it was a no brainer and PlayStation dominated the short lived Nintendo 64.
The Gamecube and PS2 generation was pretty similar in terms of what the gamers' preferences were that determined which console they purchased. Gamecube focused kiddiy games like Harvest Moon and Animal Crossing and PS2 had more games geared to teenagers and 20-somethings like Metal Gear Solid and Final Fantasy XII. But the idea remained the same, you made a choice base on what kinds of games you preferred; If you were an RPG or FPS fan, you definitely did not go with Gamecube, it came down to XBOX or PS2.
Now the generation of consoles is reaching a dividing point. Nintendo has taken a completely different route from its competitors PS3 and XBOX360 by offering wireless, motion sensing controllers that allow the gamer to be more involved in the game by having them swing the control as if swinging a racket in a game of tennis, or rolling the control like a bowling ball. The Wii's game library is also very nonthreatening and can appeal to a larger demographic; younger children and older people are now getting involved when they did not use to be. So now when someone is choosing a console, it also comes down to how they want to play games, whether interactively with the Wii or not with the PS3 and 360.
Nintendo still appeals to a kiddy crowd, like it did with Gamecube and N64, but they've captured a market of people that will not give PS3 and 360 a second balance; you can probably convince grandma to join you in a game of Cooking Mama, but it would be harder to get her to provide sniper support in Call of Duty: World at War.
Unlike previous generations, you can now separate gamers into two categories: those that play PS3 and XBOX360 (even though they hate each other) and those that play the Wii; whereas in the past you could divide gamers into their relevant consoles, this is no longer the case and dividing up gamers is much more complex than it used to be. This division is not going to go away anytime soon and is likely to get even bigger; I can see Nintendo going further away from competitors with their next console, offering even more interactive game play; I just hope Nintendo takes the time to smooth out their graphics a little the next time around, I already own a PS2.