So, I've bought my two sons an Xbox 360 for Christmas and I need some good games to go with it. They can be any rating and from any time. I have one ordered as of now, which is the new Tomb Raider game. I know I'm a bit late with the whole Xbox fad, but I think they'll enjoy it up until the 360 gets really outdated. It still has a bit to go before it runs its river dry imo.
You're really spoiled for choice here. Some of the highlights... Forza 3 (they went downhill after that), Gears of War, Max Payne 3, Fallout 3, Skyrim, Borderlands 2, Skate 3, Rock Band (and instruments), Mass Effect, Dark Souls, Sonic Generations, Assassin's Creed 2/Black Flag, Far Cry 3, Bioshock, Ninja Gaiden 2, Final Fantasy XIII, Red Dead Redemption, Dead Space, Portal 2, Rayman Origins, Deus Ex: Human Revolution, Batman: Arkham City, Mirror's Edge, The Orange Box, Grand Theft Auto V. I didn't elaborate much given the length of the list, but I can tell you more about any of the games if you want to know.
Skylanders is a good one, itcan get v expensive though collecting all the figures but you can get the first series ones quite cheap now.
If your kids are old enough to play tomb raider then they most likely would not play sky landers or Disney's take on it with the infinity stuff. Borderlands 2 game of the year edition and GTA 5 are excellent.
Rayman Origins and Legends Sonic All Stars Racing Transformed Rockband and Guitar Hero games are excellent fun to play as a family and you can often buy them for really cheap now. Just Dance is great too, if your kids like dancing.
I'm on my fourth xbox 360 now and it's my most used console, I have about 20 digital games and 87 boxed games in my collection. in no order, some faves Diablo 3 F1 2013 Borderlands 1-2 Kingdom of Amalur: Reckoning Skyrim Fable 2 Xcom:Enemy Unknown Forza 4 Just Cause 2 Minecraft Sadly some of my most fave games are rated 18 which won't be suitable probably. Ie:- Far Cry 3 GTA V The Saboteur (vastly underrated awesome game) Red Dead Redemption Mafia 2
I like Forza Horizon a lot more than any of the sim ones. Great game. As far as downloads, my favorite by far is Trials Evolution (and Trials HD before, but there's probably not a lot of reason to get both - get Evo!)
Platinum Games made some really great games for the system. Vanquish is the best TPS I've ever played. Bayonetta is good but I'm not sure if it is really kid friendly. I've also heard good things about Metal Gear Rising.
I would simply buy some Gold Subcription for the console. And let them run wild downloading demos. Then if they the next day are playing like crazy on a certain game, get them that one either as download or retail. Two controllers and Gears of War split screen or fights in Bomberman is gold though. Actually if they are into action RPGs get them Sacred 2 (not a perfect game at all, but I still spent 200+ hours on it with my GF ages ago). All 3 games mentioned are cheap and can be played co-op.