mjwman is right Picasa DOES NOT save pictures to the cloud. You can use "Picasa Web Albums" to store and share your pictures over the internet but you only get 1G of space and Picasa DO NOT guarantee the safe storage of those files.
Copy n pasted from another forum....
"Picasa Web Albums does NOT promise to protect your pictures. The terms of service says they can close the service or remove your files at any time. It's a reasonable "last chance backup" but should in no way be used as your primary backup."
With anything as valuable as photographs, I personally would back them up in more than one place. As already suggested you can back them up onto a USB stick which is definitely recommended.
I would also burn them onto CD roms if you have a burner on your laptop. Burn 2-3 copies and store them away safely in different places. If they are really precious pics of family etc maybe give a copy of one of the CD's to a friend or relative to store at their house.
You can also store them online or "In the cloud" as mentioned. I use a website called Photobucket
http://s703.beta.photobucket.com/ another good one is Flickr www.flickr.com/ You can use these sites to sort your pics into albums and save them onto an external server "In the cloud" You can even share them with family and friends.
If you use all 3 options you are covering all bases then. None of the options are 100% proof. Hard drives fail, CD's get scratched or lost and websites go down. I know how precious pictures can be so it's always best to be sure.
As for your internet favourites.......
http://www.theanswerbank.co.uk/Technology/Question1212322.html
"There is a great little free app I use to backup all of my bookmarks in case of that dreaded PC failure. It's called X-marks and is available for all of the main internet browsers. It saves all your fave bookmarks to an external server and you can even import them to several PC's.
http://www.xmarks.com/
Hope it's of some help. It's been a life saver for me several times."
RiskyB