I saw Gmail being used in this manner quite a bit among our friends with new kids (or expecting kids). I was concerned about the long term security of the memories they shared this way, which ended up being the reason I co-founded my startup, Moment Garden http://momentgarden.com .
There are surprisingly few good, secure ways to save and share memories of your kids. Particularly if you don't trust Mark Zuckerberg with your child's private data.