Is there a word for "the sunlight that streams into a room through the window, or a crack in the curtain or through a skylight"
How about sunbeams or rays of sunlight? The meaning of these terms is a little broader than the specific context you're talking about, but I can't think of a better word.
Sunbeam here is defined as:
a beam, ray, or stream of sunlight.
These are also called shafts of light
Shaft: 5. Something suggestive of a spear or arrow in appearance or configuration, as: a. A ray or beam of light.1
A shaft of light falls on the scene as the young-looking Fortinbras enters...
1 American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Crepuscular ray, while technically a reference to twilight sun, is often used figuratively for rays of sunshine in other situations.