That's an easy one.  Of course the answer is no, but very few people veer away from this standard. If you're feeling adventurous and want to break away from the pack  here are some suggestions.

Consider practicalities 
When you decide to paint your ceiling a colour you need to think about  how that colour will flow into other rooms both physically and visually.

Is there a place (e.g., molding or beam) where you can stop the colour? 
      Minimalist kitchen design modern kitchen
       The ceiling in the kitchen is on a different plane than the living room, thus providing an easy break for painting.
      How will the colour look when viewed from the next room or rooms?
        In the room above the ceiling is acting as an "accent wall" and flows nicely into the living room.  The same blue is used in hints around the room creating a visual flow.

        Will you have to  change the colour again when you paint your walls? 
        Chances are you will.  Are you up to painting several coats to cover a colour?


        Is your ceiling in good condition?  
        Flaws will show up more with darker colours.

          Consider ceiling height
          How high is your ceiling?  Nine feet or above will provide lots of height for darker or warmer colours.

          Beverly Bradshaw Interiors, Seattle, WA eclectic dining room

          Luxurious Gold and Silver Painted Dining Room Ceiling traditional dining room

           However, if you have standard ceilings (8 feet) and your rooms are smallish you might consider lighter, cooler colours to help the ceiling recede and give the feeling of greater distance.


           
            Traditional Home
          Blue seems to be a popular ceiling colour.


          Consider your  wall colour

          If you really want to paint your ceiling and aren't sure which colour to choose, take the cue from your wall colour and simply go several values lighter.

           Toby Fairley 

          Or keep the ceiling and walls the same colour and break it up with crown moulding.....

           or go a value or two darker for the ceiling.


          Consider your trim colour
           If you have a trim colour other than white/cream, look to it for ideas for your ceiling.These room have a very pulled together look by using the trim  colour  as a branching off point.

          Real Simple
           The ceiling is darker than the trim colour

          Residences in DeBordieu Colony, Georgetown, SC traditional living room

           The ceiling is the same colour as the trim. 


          Consider your accessories 
          This is where things could get exciting...
          tineke triggs contemporary bedroom

          Can you imagine this room with a red ceiling?
          Hollywood Residence eclectic dining room
           
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