I will await Llama's opinion.
Wow. Someone's actually waiting for my opinion! It was bound to happen sooner or later. ;-)
OK, The Eicar Test String (developed by the European Institute for Computer Antivirus Researchas, hence the name) is basically something that all antivirus programs detect as a virus by a "gentlemen's agreement." This string really isn't dangerous in any way, but it is always included as one of the viruses in a virus definition file for testing purposes. Theoretically, it is the only "false positive" an AV utility should detect, since it really isn't harmful but it is flagged as if it is.
For example, if you are concerned that something has "knocked out" your antivirus program, you could try to save a file with The Eicar Test String and see if your AV software flags it as a virus. If it doesn't do anything, you should suspect something is wrong with your AV software's background scanner. If you manually scan it and it doesn't create an alarm, you should suspect something is wrong with the foreground scanner.
If you don't feel like finding and messing around with real viruses, it is a perfectly fine way to test for minimum AV functionality.
But again, it isn't dangerous, any more than pointing your finger at someone and saying "Bang!" is dangerous.
For the record, I never use The Eicar Test String to test anti-malware products. In fact, I don't even bother creating a file with it, since I have tens of thousands of real viruses I can test with that I can use to generate some detection statistics of my own.
-Llama