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 cartridgeblowing in an NES cartridge.