Why does my internet always quit on me?

[Tony RB]

"when everyone in my family is using the internet"

If several people are using wireless, you have congestion.

Other devices or appliances are putting out radio waves that cause interference. And these could be in a neighboring property. Or someone parked in a car nearby trying to eavesdrop.

You are competing with everyone else for bandwidth.

Any of them or all of them could be using a huge amount of the many megabits-per-second available, like watching a movie, opening several pages on a website, all of which contain a lot of advertising images and flash-animated ads.

Another possibility is the router has a bad port - the electronics on that port just don't quite work right. To test this swap the cables for your port and one of the others.
This won't work for wireless, though.