I've tried to burn some Divx DVD movies, but it doesn't work in my DVD player. What is there problem out there? Can't DVD players read Divx movies? Or I've just to burn them in VCD's, if I do that, then the quality will be decreased.

a list of DivX certified DVD players is here
Some other DVDplayer will play DivX format discs but mainly the newers ones
If you want to play a DivX film on a DVD player that doesnt support DivX format you will have to encode it to DVD format using Nero or WinAvi