It has "always" been common to blow into the cartridges when there as been problem with game not starting. It's usualy effective just then, but it's not a good thing to do after some time.
The reason is that when you blow you blow some of the dust further in to the cartridge. You also get a certain amount of moisture and this causes more dust to get stuck to the contact plate. After a wile this dust will get to the connector inside your NES and this will be "damaged". If so happens you have to replace your connector. This is an easy job to do, so not worry. But when you have replaced, itæs a good thing to know that your games are clean som your connector will last longer.
To clean your games, just get som "clean" alchol and some q-tips. Do not use to much alchol because it's just to get the q-tips wet. Clean both sides of the contact plate and make sure not to get any of the cotton from the q-tips stuck on the plate. It drys quickly, so you are good to go just aftre finnished cleaning :) Happy gaming!