Yes, Actually, you can. But you are going to have to have an European PS2. =\
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You can't play PlayStation games on the Internet, but if you have a PlayStation 3, you can go on the PlayStation network and play with other people through the Internet.
No Runescape is an Internet MMORPG. It is only playable on the PC/Mac.
Playstation 2 does have an internet connection and there was once an official Netflix disc for streaming in Brazil only. Playstation 2 even offers 1080p video output via component cable, making it a perfect fit as a streaming client. Unfortunately though, the service was stopped in the year of 2012 as there was Playstation 3 which offered all the things Sony has promised to realise in the age of Playstation 2 (including usage of Playstation 2 as a personal computer, linux kits were sold at that time).
go to PlayStation store and search skate 2 and download the demo or buy and of course you need Internet
PlayStation x PlayStation 1 PlayStation 2 PlayStation 2 slim PlayStation 3 PlayStation 3 slim Coming soon - PlayStation 4