I'm an avid gamer myself, and have been since the original Nintendo (I'm 22 now) so I can provide you some insight on this, as I('ve) own(ed) them all.
I think that for kids, the Wii is a hands down winner. It's a reliable system, innovative, and VERY family friendly. Nintendo also has excellent tech support were anything to go wrong (which I'm 99.9% sure it wouldn't). It also happens to be the cheapest at $250. It comes with the Wii Sports game packaged in, and it's very easy for anyone to pick up and play. It also plays the last generation Gamecube games. The only downside to the Wii is that they are so popular, they're still hard to find in some places.
The Playstation 3 is excellent, but at the moment there isn't a big selection of games on it. And especially not family-friendly ones. It's also the most expensive, but has a built in Blu-Ray player which is the wave of the future as far as movies go, built in Wi-Fi, 60-80gig hard drive, DVD upscaling, photo storage, mp3 storage, reads MPGs, JPEGs to slideshows, and on the current models backwards compatibility so it plays all PS1/PS2 games as well. It's pretty much the complete package as a home-entertainment system. $450-500 starting price though, with no game.
The XBox 360 I cannot reccomend. There are a ton of excellent games on the console, but the Xbox 360 is
EXTREMELY unreliable. I can not stress enough that you avoid this system. I had 3 of them, and they all 3 failed before I gave up on it and picked up a PS3 to compliment my Wii. While the games are great, the system itself is extremely flawed internally and has major overheating issues. It has been acknowledged that the 360 has a 33-40%
FAILURE rate. Microsoft also confirmed they are losing
BILLIONS in repair costs and warranty extensions. I (or most others) just simply cannot justify spending $400 on a machine thats a roll of the dice. You shouldn't spend that kind of money on something that has a 1 in 3 chance of going bad, and quickly at that. While Microsoft has owned up and extended their warranty to 3 years, it is a royal pain dealing with them. Sitting on hold, getting non-english speaking tech support, refusal of claims etc etc. I can't force a decision, and I'm not trying to hate on them because there are good games for it and theres a lot who are happy with the 360, but do yourself a favor and avoid this one. From seekingalpha.com:
Microsoft (MSFT) said Thursday that it will write off $1.15 billion to extend the XBox 360 warranty to three years and reimburse owners for repairs.
Some have estimated that as many as one third of XBox 360's sold to date have failed. And the amount of money being allocated -- $100 per XBox 360 sold -- would allow Microsoft to replace every third XBox with a new base one at retail prices, so that estimate may well be accurate.
But that said, all is not well in XBox 360 land. If you look at the graph below Q2 2007 now is the second quarter in a row where XBox 360 sales have declined year over year, and Microsoft admitted in its statement Thursday evening that it fell short of its sales goals. And Microsoft was losing money hand over fist with XBox 360 before taking another billion dollars in warranty expenses.
So in closing, get yourself a Wii. You and your kids will be MUCH happier in the long run with it in my opinion. Extra controllers etc are an additional cost for all systems so don't let that be a deciding factor.