Lesson One: Save. Save your work as you work on it.
Lesson Two: Back up important stuff.
Backing up your important stuff is something that everybody eventually realizes they need to do, but often people are not sure how they should do it. How you back something up should reflect how important that data is. If it is your password database (encrypted I trust) then sending an email to yourself is fine. If it is all your documents and pictures and tax returns, making an extra copy on your computer is not safe enough and it is likely too much data to email yourself.
For most backups, I now recommend people buy a USB external drive. They range from fifty to a couple hundred dollars, but a 500 GB drive is enough for almost everything a person could want to save and it will run between $50 and $100. Prices are always coming down, so you may be able to get one even cheaper. You should back up important data to a second hard drive on a regular basis. If it is data important enough that the risk of loosing it in a fire is a real concern, then you should get two or even three and rotate them to a different location. One example is to put one in your car, have one at work and have one plugged into your computer. If it is vital stuff on a daily basis, you should take the fresh backup to your car in the morning, swap it at work and plug the one from work in when you get home at night.
If your data needs to be kept secure, I recommend TrueCrypt for Windows users and LUKS for Linux users. I'm sure Mac users have an option, I just don't have sufficient experience to make a recommendation. LUKS and TrueCrypt make it possible to encrypt an entire drive or whatever portion you prefer so that nobody (NOBODY) without the password can open it. It is possible to use keys on external devices if you need extra paranoia, and with TrueCrypt you can even bury very secure stuff inside of fake secure stuff.
I do not recommend cloud storage backup services like Carbonite. They may be great for a few people, but most people will back up a lot more stuff and do it more reliably if they know exactly what is going on the backup drive.
For the cash strapped, you can back up really essential things to either your free email account or a thumb drive. Obviously they have much less capacity, but you can get a good backup with a $15 usb thumb drive that holds 4GB of data.
For the adventurous, you can backup up your data over a network or internet connection between computers with permanent drives. The only thing to bear in mind from my voice of experience is that you NEED to know what RAID you're using if you're relying on it. Twice I've been burned by systems set up with RAID 0 where they were supposed to be RAID5. At least twice I've recovered from drive failures that had a good RAID (1 or 5) and probably other times when I've been able to swap a drive at warning rather than failure.
For the network backups, I can also recommend SCP because it is dead easy and OpenVPN because it can work with about any protocol. I wouldn't recommend FTPS or CIFS or NFS if you're using an internet backup unless you're putting them through a VPN connection.