Thankfully both Internet Explorer and Mozilla Firefox have fixes for instability and crashes. But before you get too far, let's make sure that you have the latest version of Internet Explorer and Mozilla Firefox.
In Internet Explorer, go to the Help menu and click on "About Internet Explorer." If you don't have a menu bar, click on the question mark just to the right of "tools" and then click "About Internet Explorer". At the time of this writing, the latest version is 8. You can also go to Windows Update and make sure that there are no updates available.
Firefox generally updates itself within versions, but you could be running a very old version. Click on "Help" and then "About Mozilla Firefox" and make sure that the version you have matches the latest version available at http://www.getfirefox.com. If not, download and install the latest version.
Lastly, you can reset the browsers to their default states. In Internet Explorer, go to Tools, Internet Options, Advanced, and then click "Reset" and "Reset" again. That will reset IE to its default state without any extra addons. Your preferences and personal data will be retained.
For Firefox go to your start menu in Windows XP, or just click Start in Vista and 7. In XP, click on "run" and then type in "firefox -safe-mode" and press enter. In Vista and 7, just type "firefox -safe-mode" and press Enter. Select the option "Reset all Preferences to Firefox defaults" and then click "make changes and restart". Done!