The term 'Web-Safe' dates back to when early monitors could only display 256 colors (but there are only 216) because they were developed by maths in steps of #000033 and not really for their visual effect. The other 40 would not have been cross browser compatible.
Not everyone had 16 million colors on their computer, but the vast majority will have them now. It doesn't mean that the colors will display the same hue on all monitor screens. Today, web safe colors are not important and only shown here to give an idea of the hexadecimal values.
If you want to print this chart out for future reference, you'll need to set your Print Background Colors and Images Settings
Control Panel > Internet Properties > Advanced > Printing or you'll just get a page of hexadecimal numbers.