I had no problem opening US trading accounts with Interactive Brokers whilst I was in Dubai for myself and my wife. The only issue if you are investing in US stocks and funds is that the US has no tax treaty with the UAE so all Dividends are subject to 30% Withholding Tax. I also opened an account with OptionsXpress who are now Schwab.
For European markets I had a trading account with TD Waterhouse in Luxembourg (I think they used to be Internax) but I would hesitate to recommend them.