Running Internet Explorer 6, Internet Explorer 7, and Internet Explorer 8 on the same machine

I wouldn't do it. Use virtual PCs instead. It might take a little setup, but you'll thank yourself in the long run. In my experience, you can't really get them cleanly installed side by side and unless they are standalone installs you can't really verify that it is 100% true-to-browser rendering.

Update: Looks like one of the better ways to accomplish this (if running Windows 7) is using Windows XP mode to set up multiple virtual machines: Testing Multiple Versions of IE on one PC at the IEBlog.

Update 2: (11/2014) There are new solutions since this was last updated. Microsoft now provides VMs for any environment to test multiple versions of IE: Modern.IE

Nobody mentioned this, but IETester is a great tool. It supports Internet Explorer 5.5, 6, 7 and 8RC1. The rendering matches the corresponding browsers. At least I haven't found any discrepancies yet.

I normally use it to do a basic check of the layout. I still need VMs to debug JavaScript or to use the Developer Toolbar with a specific Internet Explorer version.

You can use the new MS Expression Web SuperPreview

_{(source: istartedsomething.com)}

If you do not want to spend money on MS Expression Web, you can download Microsoft Expression Web SuperPreview for Windows Internet Explorer completely free. The only restriction is that after the trial expires you can't compare to non IE browsers.