Most states have college savings programs that are tax exempt or tax deferred. The returns may be higher than savings bonds but the accounts are not always guaranted by the government. Some programs do not have a gift tax attached to them. Most do not allow you to add money after the child turns 18. Most have an upper age limit too, an age by which the money MUST be dispersed. You would have to check out what programs are available for your state doing a Google.

http://home.okstate.edu/homepages.nsf/toc/statesavingsplans

http://www.google.com/search?hl=en&hs=tqZ&client=opera&rls=en&sa=X&oi=spell&resnum=0amp;ct=result&cd=1&q=deferred+college+saving+program&spell=1

You may have more control over a college account account than with savings bonds.

Are you giving the money "no strings attached" or do you want to see it used for something specific like college?

Savings bonds can be made out in just the childs name or you can have them made out jointly or a POD. Check to see if your state charges income tax on the savings bond interest - some do and some don't.

It's great for you to start saving for her--but I have to present a family situation for you to consider.

One Grandma, 2 families of grandchildren. Every year Grandma gave each child a $100 bond on their birthday. This wasn't easy for her--she saved $1 per week, for each grandchild so she could do this for them. One family put the bonds aside, and when the interest rates warranted it, cashed in the bonds and put them in a higher-paying savings account. That grandchild paid for about half of one year of college tuition with those bonds. The other family? The mom allowed the kids to cash the bonds early, and to fritter the money away. Also, the mom of the second family used to take her children's monetary gifts and spend them as SHE wanted to for the kids. The first mom put every penny her daughter was given as a gift into a savings account when the child was too young to spend money--and when the child got older, she still had to put a portion of her birthday and Christmas money into the bank.

Some people believe that money given to children is for them to spend, some feel it's to save for their education. And sometimes, one parent can feel one way, one the other--so you're never quite sure the money will be used as you intended it to be. And I've known a few parents who even took their children's money to spend on themselves, justifying it by saying they were putting it toward bills for the house where the children live. Sometimes money does strange, unexpected things to people we know and love, and thought we could trust.

Obviously, my point is that if your plan is to put this money aside for the children's future, you need to retain some sort of control over it. Even if the parents are responsible, it's possible the kids would cash their bonds in in their teens to buy a junk car, or to pay for a spring break in Cancun. I'd probably choose to put the money into a custodial savings account in the child's name, with myself as the trustee.

Azzalea is sure right about the different family styles--add another --the kids get on drugs and blow through any money they get immediately.
Retaining control is always a good idea--a savings acct you own but on your death it goes to somebody else (pay on death account) or custodial account. You can buy savings bonds with joint names, and you keep them in your possession. If you have control you can change the gift if the kid changes. I am always amazed at how ungrateful & spoiled some kids turn out; people should try to avoid leaving anything to those kids.