Think about it. BeanieBabies are trading collectables (with some entertainment value for kids) - and MisterSuitcase hoards them and watches the market valuation and waits for lines to be discontinued... It's just like BubbleGum? cards were. And out of that, we got MagicTheGathering.
The only games I know of that use BeanieBabies are:
Cuddle Warfare - (published in an old dragon - wargaming using teddies)
Throwing them around (a variant on 52 card pickup, perhaps?)
Vitenka's sister has multiple giant yellow beanie fish. They have a speaker implanted in them. When you shake fish, FishSaysMoo.