My kids have had their own Gmail addresses since they were about five years old. I set them up with accounts, added family and close friends to their contact list, and showed them how to communicate with Grandma, their uncles, etc. There's nothing cooler than getting an email from your five year old chock full of heart and rainbow icons.
My son has had his account for five years now, and it's full of history. I'll share YouTube clips with them, pictures, messages. It's a great digital archive of his early years, and he can keep that address forever.
Things haven't gone as smoothly for my daughter. At some point, Google prompted her to enter her birth date. She was born in 2004, and disclosed that to Google. Immediately, Google locked her out of her account. Apparently, you can't have a Gmail account unless you're at least 13 years old.
What irks me is that the account was suspended immediately. There was no opportunity to back-up emails. It was an instant "you're too young - sorry" and all was lost.
Michelle has a new Gmail account, and I've instructed her and James to never disclose their age to Google. They love having their own email account and using Google Chat and it's easy for me to monitor everything to ensure they're using it appropriately.
Google themselves seem to promote the idea of Gmail as a means of capturing a child's history, but in reality, they'll terminate such an account without warning.
Mamas, don't let your babies disclose their birth year to Google.