Yes. Google server data is replicated among servers in several different data centers across the planet. They even have tape backups and other proprietary methods to ensure the security of your data.
http://www.youtube.com/wa
I would be more worried about any photos that are not on their servers.
You can store photos in Google Docs, but I'd recommend using Picasa (soon to be renamed Google Photos). It's a better way to see them all and share them.
If you are using Google+, you can turn on instant upload on your android device and any photos you take will be automatically uploaded to Picasa.
Sleep well.
Can I sleep soundly at night if I store my family photos within Google Docs and nowhere else?
