So after finally be forced into it, I will be upgrading my Macbook from Leopard to Mountain Lion, with the required stop off at Snow Leopard (already bought the disk). However, after having the Macbook for four years, I have a lot of e-mails, address book entries, iCal dates, etc. that I'd like to keep. How do I save these? Do they stay on the computer after the upgrades?
First, you should always be backing up your computer. With a Mac it is super easy with Time Machine. So if you haven't been doing it, shame on you. I would highly recommend doing a full backup using Time Machine to an external Hard Drive before doing your upgrade(s). Everything SHOULD be there after you upgrade, all your emails and contacts and calendar information, however there is always a chance to loose data and thats where the back up comes in handy.
What Tom said. All of your files will still be there when you go through the upgrades as long as you don't format your hard drive somewhere along the way. I think that you get the option of doing a clean install or an upgrade... do the upgrade. That said Tom is also right in that you should be backing up on a regular basis and especially before an upgrade because you never know when something may go wrong and your disk may get pooched.
There are also "cloud" services like iBackup, which for a fee will do automatic backups of your data. Failing that, Google Drive or Dropbox can be used to sync your data to the cloud (especially nice if you have more than one computer or an iOS device). Cloud storage has the added advantage of being out of danger of being lost if your house burns down. DVD backups are nice, but they'll melt if you forgot to turn off the gas. Also, make sure you have good installers for your various applications, just in case.