Popular belief among those of us who remember the original NES held that that blowing into an NES cartridge removed dust from the contacts, which allowed a better connection to the system.  In practice, the method was similar to the following:

 - Plug in cartridge, turn on system
 - Curse when system does not work
 - Pull out cartridge, blow
 - Re-seat cartridge, try system again

In a few cases, blowing may have actually removed dust, but the truth is that **most of the time, what actually fixed the problem was the act of pulling the cartridge out and putting it back in.**

As the original NES required you to put the cartridge in and then down, another common trick was to shove a second cartridge in the slot on top of the first one, which prevented the bottom (game) cartridge from slipping.

Finally, Mental Floss has a detail analysis of the effects of [blowing in an NES cartridge][1].


  [1]: http://www.mentalfloss.com/blogs/archives/142550