Alright, so replaced your NES pin connector, but the games still aren't playing, so now what?
Ah yes, blowing in the cartridge, the old standby. While this does work, it can have negative long term effects. The biggest one is corrosion, since you're blowing into the cartridge you're getting moisture on the contacts, which in not good. Digital Press did a test on whether or not blowing on the cartridge would cause corrosion, and you can either go here to read the whole thing, or look at this image after the jump which sums it all up.
Yikes! (Image courtesy of Digitpress.com)
Anyways, to avoid this you need to clean cartridges with something other than your own hot air. The best thing you can use is rubbing alcohol, at least 70% should do it. And you're gonna need something to clean with (just pouring it on will annihilate your game), I suggest Q-tips. Take 2 Q-tips and use a sprayer to spray some alcohol on them, just enough to wet them, they don't need to be soaking wet. Now rub the contacts vigorously (don't worry, it won't hurt it, I promise) until it leaves no more crap on the Q-tips. After that, rub the dry side of the Q-tips over the contacts to get any excess off. Now repeat that with the other side and you should be good to go!
Now, this can be done with any game cartridge, so go break out that SNES, Genesis, Atari 2600, Neo Geo (you freakin rich people), or whatever old system you have and get those game back into commission!