For Singapore, there's also an arcade in the Hereen on Orchard, hidden away a few floors up behind all the shops targeting cutting edge kiddes, and one in Suntec near the Eng Wah Cinema. There was a good one in Plaza Singapura too, but I think that one has closed down now. As jpatokal mentioned though, there's nothing particuarly exotic in these arcades, but fun enough (though even Hong Kong has a better range of games, and Japan definitely has more to explore

).