Any site which pays you for making highscore in games..........

There are lots but you have to pay some amount. Try worldwinner.

hi there! most gaming sites involve real money, but i know exactly of one which is free. you have the option to play one on one with another player or submit your high score and win the jackpot. i just joined recently and got paid at once. they are legit, plus the admin and other players are very supportive. add me as a friend for the link if you're interested, and i'll be very much willing to guide you and give you the tips to earn on this site.

You can try umefriends, you can find there dozens of flash games, and they pay you for each match you have, also if you don't break the highscore ;)