Do I need a grounded electrical outlet for a laptop and computer monitor?
For one, it probably violates your local electrical/fire code, your fire warden would be upset. They would be more upset if they found you dead (however unlikely, more likely if you don't ground devices) 

Another reason not to do this is there is no where for fault currents to go. Laptop power supplies are usually doubly insulated and don't need a ground because fault current's can't reach the user (two prong power supplies). Monitors usually aren't. Either way if there is a third prong, it needs to be grounded for safety reasons.

It's also a good idea to ground to prevent noise and to give static electricity a pathway back to earth.