Never, never blow in the cartridges. That only causes more spit, and dirt to get caught up in the cartridge and cover/destroy the contacts. Think about this, if you're not the original owner of the games, some little kid 15-20 years ago was blowing in that cart. Then the next owners and the next owners, and now you. Now you've got 15 years of spit/dirt built up on those contacts. Not something pretty to think about.
The best method that I know will work is using rubbing alcohol and q-tips. Does the job every time.