How dangerous is it to leave spyware on your computer?
We found we had spyware on our computer and used Yahoo's anti spyware program. However, not all of it was removed. We keep getting a message that says something like "there is a pest imbedded in your computer." Following the instructions to remove it didn't work. Is it really dangerous just to leave it there?

"there is a pest imbedded in your computer." Sounds like you have one of those fake antispyware or antivirus that just wants to trick you into buying their program that doesn’t work anyway. Meanwhile it’s downloading some serious malware that can steal your sensitive information. So yes you need to get rid of it.
What program did it recommend? There are a bunch of them out there right now. How to fix it depends in which one it is. You can find a list of fixes for most of them here: http://www.bleepingcomputer.com/forums/index.php?act=SF&s=&f=55
If you can’t find the right one, or even if you think you might be rid of it, I recommend going thru this process also. http://www.bleepingcomputer.com/forums/topic34773.html
Most of it leaves behind stuff you don’t even know is there.