Not sure if you can download official games yet on to your PSP from any authorised site. However three things to note
1) The official PSP website has extras you can download for free
2) You can look into 'Homebrew' programmes that will allow you to download games to your PSP. However note, this is illegal and to the untrained person, can prove awkward to set up
3) There is official word that Sony will soon be allowing people to get PS1 games for their PSP. Either by selling them in the shops or even quite possible being downloaded on to your memory stick....that could be what yoru after.