We have a 3 and 5 year old and I opened a joint savings account through ING, now CapitalOne 360, for both of them soon after they were born (through one of the "sales" where there was an account-opening bonus). A couple years ago when there was a similar bonus incentive I opened a custodial Sharebuilder account for each of them and now everything goes into that with automatic investment purchases when the savings account gets to a given amount. They've got $1200-1400 just from the little monetary gifts they get at holidays and birthdays (and these aren't huge amounts....$5-20 here and there adds up!). Every time I transfer the gift amount from our account to theirs, I enter the giver and occasion in the memo line so there's a history of who gave what and when. Kind of nice for when the kids are older...
We also have a 529 account for each them (we're also in WA and the GET program is pretty good) but all of our family is in Canada so giving certificates for them to contribute to that was complicated. However, if they were in the US and somewhat computer literate, we'd potentially have done that instead.
I don't know how to not ask for cash instead of toys. We just let family members know that these were in place and that all monetary gifts would be deposited, and causally mentioned how much stuff they already had. We've found that they usually get a gift to open as well as money. However, the amount of stuff has been toned down considerably, and the gifters feel good knowing that they'll have the money (and appreciate it way more) when they're older.