Interactive brokers and Tradestation securities open for every country. Schwab open account for every country but 25k Minimum. TD ameritrade also open for most countries. they have different website for different region. if you are in Asia, you need to visit TD ameritrade website in singapore. both going to merge soon. Fidelity open for US only. No idea about E*Trade, they going to merge with Morgan Stanley. So you neede to avoid them for now
Schwab only allows Germany/Switzerland/UK (maybe one or two more that i missed) as far as Europe goes.
CenterPoint seems to be good because of the clearing firms but the problem is that limited trading hours. :/ They open at 7:30 am i guess and you miss 3:30 hours by that...