Once you have made the decision to trust online, or "the cloud" with your data backups, there are 2 ways you can go:
1. Backup your entire computer
This is relatively cheap to do ($ 5 / month), but this may be killing a fly with a sledgehammer if you only want pictures and emails saved.
Online backup has been around for a few years but is becoming more and more popular of late, as people are feeling warm and cozy about internet transactions.
Several companies providing this service are Mozy, Carbonite, and SugarSync.
They have all been around for years and backup a shockingly high number of petabytes of people's data.
Your data is all encrypted from start to finish – so it is actually safer than the unencrypted data on your computer.
2. Backup only the files you really treasure or have to have
This can be done either through a variety of online services.
To me, pictures and emails are my record of the past and I do not want to risk losing them, even a little bit. I find myself continuously search my emails for projects I have done and people's names I can not seem to remember.
I really need to keep them all and I know I am a coffee spill or theft of my laptop away from losing it all if I do not backup.
If you are an Apple user, the easiest way for you to save pictures is via iTunes or iPhotos. Very easy to setup and it's free. (Although, your copy will actually be stored on your computer.)
The easiest way to save emails is through Gmail. Either use Gmail for all your emails or sync your Outlook emails with Google Apps Migration for Outlook.
In conclusion, whether pics, emails, or other it is essential that you backup your very important data or, just take the step and backup all of your data. If you take this step you will not believe how stress reducing it will be.