I know TD Ameritrade offers it and I suspect most brokers do. Look on your order screen for type of order. You should have, Market, Limit, GTC (good til cancel) and I have choice of after market and pre market.
I think most do. I know that TD Ameritrade (think or swim) and Scottrade and Interactive Brokers do. Interactive Brokers: How to Enable Trading Outside of Regular Trading Hours http://ibkb.interactivebrokers.com/node/1274