Game cartridges, such as games for Nintendo, Super Nintendo, Genesis, N64, or even small ones like Gameboy, Gameboy Advanced or Gameboy Color, are generally very tough.
However, it is still possible that a game might stop working. Most of the time, if it a rather easy fix, rest assured.
The first thing you want to try is to clean the heads of the board in the cart. That is because it could simply be dirty and preventing the connection with the console.
To do that you will need two things: isopropyl alcohol (rubbing alcool) + cotton swabs (Q-tips)
Try to use alcohol that has the highest % you can find. Dip your cotton swab in it, remove the excess (it shouldn’t be dripping) and then rub the heads of the board (the “metallic teeth”) at the bottom of the cart, upside and downside.
If the cotton swab gets dirty, repeat with another one, until the heads are clean. Then try your game again. A LOT of game carts will start working again after being cleaned that way.
If many (or all) games (of the same type) refuse to work in your game system, it is possible that it is your console that is dirty inside. To clean it, do what we just explained and clean a game cartridge, then put it in the console. Take it out, clean it again. Put it back in, out, clean again. Rinse and repeat a few times, and it might work.
Now sometimes, small games will stop saving your progress, or you will find that the progress you had saved the last time you used it is gone. That is usually the internal battery that is depleted. Luckily, it can be replaced.