Play on line Shanghai Dynasty for free.   No account needed.   There are two versions - a short one for kids or the longer one called Shanghai.

Go to this site and click on the version you would like in the lower left hand corner.  Then click on matching tiles to make the pairs disappear until you clear the board.

http://www.castlemountains.com/index.cfm?action=sendcard&card_id=1439&type_id=3