There are DAX and Eurostoxx traders here, and people who have posted about dabbling with the Hang Seng index. All these are available through Interactive Brokers, or any other broker really. The prices for the intraday exchange data, contract, and amount of margin you need will depend on what you will trade...
and most of the electronic futures contracts here trade round the clock, although the ES is the only one with enough liquidity throughout the day and night to move significantly (that's just my opinion, though. I won't touch RBOB,and other people talk of trading oil after hours)...
Disclosure: I have an account with IB
EDIT: Surdo is right: forex pairs move significantly during time periods other than EST RTH, I'm told.