I haven't read the other responses - sorry if this is a duplicate....
How about gifting them some type of lessons (ski, swim, skating, sports) or gift certificates to a local Museum, pottery painting place, or a place like Pump It Up?
Or you could open up a Mututal Fund or some type of College Savings account that you could deposit directly into in the years to come, that way their cash can't be spent on video games.
I heard recently someone say, "Give them something to DO not something to have". I intend to pass this piece of information along to my friends and family who are always asking what they can get my boys at Christmas and their birthdays.