Blue Disks
Some of the earliest PS2 games were known as the "Blue Disk" games because the bottom of the disc featured a blue colored backing. This was one of the earliest causes of PS2 errors. The disk color and burning process made it hard for the laser to read them. Avoid using these discs and look for releases of the games instead of buying used blue disc PS2 games.
Old PS 2
The first generation of the PS2 was bulky and made it hard to actually get inside in case of an error. After a lot of use the laser needs cleaning in order to properly play games. If your PS2 is not reading the disc for multiple games, use a screw driver to carefully open up the system and gently clean the laser with a tissue. Test a game in the PS2 before connecting all of the parts again.
DVD Playing
The PS2 was created primarily for game playing, but DVDs could also be played in the console. Movies needs a constant spinning of the disc in order to load content, so if you play a lot of DVDs in your PS2, the laser could have gotten burnt out and made it unable to read discs.
New PS2 Model
The newest PS2, the PS2 slim is a much slower and better performing system. There is direct access to the laser inside of the system and the laser is upgraded with little problems. If you come across a disc read error with this model, make sure that your disc is clean and scratch-free. Use a scratch remover in order to clean any discs that do not play in this system.
Considerations
If you have tried multiple options and the PS2 still will not read discs, it is better to start over with a new crisp system. The release of the PS3 has knocked down the PS2 console price and games are cheaper as well. Eventually fixed problems may come back again, creating more of a hassle.