"I am in bed" = I am under the covers. "I am on the bed" = I am lying on top of the covers.

As Leigh pointed out, the are both correct depending on context. One typically says they are "in bed" when they are under the covers and are about to go to sleep. Although, in the morning when you wake up, you can still be in bed. It means you are under the covers still and are trying to wake up enough to get out of bed and on with your day. :)

On