This was historically dealt with by recommending that your home cinema arrangement was established in a room over which you had significant control over the light sources, perhaps with heavy curtains, black-out blinds, or because your home cinema was established in the basement.

Fortunately improvements in HD projector design and manufacture have meant that projector brightness is not as significant an issue as it once was.  A typical HD projector will have a lumens value of around 1,500 which should be adequate for most domestic environments, although projectors up to 3,000 lumens can be purchased.

photo credit: exquisitur