In Hardware

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It's probably not a matter of worn pins on the games themselves... It's probably the console itself. You probably have a bad 72-pin connector. You can do one of two things...

1. Take your NES apart, and get to where you can see the connectors. Then, use a tiny screwdriver or something small to pry with to pull the pins that are down more so than the others to make them flush with the others. This will establish a better connection with the games.

2. Find a site or auction that has a 72-pin connector, and bid or buy...

If you don't think you can do the first suggestion, then I would do the second one if I was you... No need in ruining a perfectly good NES!

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If there's a problem with the games, you just can try to clean the pins.
When the pins are broke or something, there might be no hope.