If you need to test your RAM, Microsoft offer a free tool called windiag. The tool has its own loader, so it works autonomously for Intel or AMD processors, this means it works for Intel Macs or Linux Systems just as well as for Windows machines. You can download the ISO file here, burn a bootable CD and boot your computer from the CD. That's it.

Go here for the German windiag website.

And here's a reminder on how to burn an ISO disc image in Mac OS X:

1. Insert a blank disc.
2. Start Disk Utility.
3. From the File menu, choose Open Disk Image and select the ISO to be burned.
4. In the list of volumes, you will now see an item representing the ISO file. Select it.
5. Click the Burn button and follow the instructions.

This reminder is courtesy of vocaro on macosxhints.com. Thanks!

Not so long ago I upgraded a 12" PowerBook from Tiger to Leopard OS X, resulting in a blue screen on restart right after installation.
The cause was the Unsanity Application Enhancer installed on the old system. If you do an upgrade, check if you have Application Enhancer (a helper Extension in System Preferences, used for Applications like Airfoil for example) installed and uninstall it if its there.

In case the blue screen is already there, help is provided on the Apple's Support Discussions:

http://discussions.apple.com/thread.jspa?threadID=1197402&tstart=45

Boot your blue screen Mac in Firewire-mode if possible (by pressing T on startup), connect to another computer and remove the following files:

/Library/Preference Panes/Application Enhancer.prefpane
/Library/Frameworks/Application Enhancer.framework
/System/Library/SystemConfiguration/Application Enhancer.bundle
/Library/Preferences/com.unsanity.ape.plist

If Firewire-mode doesn't work you may have to remove your hard disk and place it in an external drive to sort t out. For me Firewire-mode worked fine though.