Note
This issue is about sunlight. For the related block light issue, see MC-102162.
The bug
Certain blocks "save" sunlight, emiting it even after the original source has been removed. This creates an annoying glowing spot and is very difficult to clean up given that the blocks are not obviously the source of the glowing (and that it can chain between multiple of them).
Affected blocks (may be incomplete)
Water
Leaves
Cobweb
Magma
Lit redstone ore
Lit furnace
Powered redstone lamp
Glowstone
Sea lantern
Jack-o-lantern
Reproduction
Build a sealed room without any lights in it with a single layer between it and the sky.
Place one of the effected blocks on the floor.
Break the ceiling block above that block.
Replace the ceiling block.
Observe that the room remains lit, despite the lack of a light source.
Notes
-In versions prior to 1.7.2ish, this also affected other blocks (for sure glowstone, lit redstone ore, lit furnaces, and jack 'o lanterns — mostly, blocks that exhibit MC-102162 but also similar blocks that emit full light). In 1.7.2 it was fixed for those blocks. Incidentally, 1.7.2 had a fix that removed an x-ray effect when inside of glowstone; it's possible that those are related.- this issue returned for 1.11.2
Lava is not effected, despite also being a fluid.
Water only finicky about being affected; if it's in a pit it doesn't get affected but if it's above the ground it is.
This only happens when the block is in direct sunlight; if it's next to the sunlight but not exposed to the sun it doesn't seem to happen.
Demos
Demonstration from the Minecraft version 1.4.5 : http://youtu.be/8nTd1KbbrLA
EDIT SEPT 19 2015: Demonstration from the Minecraft version 15w38b: https://youtu.be/bPUdssOvU78
Related issues
is duplicated by
relates to
Comments

Confirmed

Is this still a concern in the latest Minecraft version 14w04b? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
can confirm for 14w21b
I can also confirm for 14w21b. Additionally powered redstone blocks act as transparent and exhibit this behavior. It seems that transparent blocks often do not update their light level, thus preserving previous sky light levels.
I've had this same problem with stained glass but am having trouble duplicating it.

this is still a problem in 1.7.10 and 14w28b
EDIT: wait no, I was wrong
Bug still confirmed in 15w38b. It's been 3 years, maybe it's time to fix it, Mojang?
Confirmed in 15w47c. It interferes with the operation of daylight sensors, which think the "saved" light from glowstone, etc. are daylight and emit a signal where there should be none. It's also difficult to fix once it occurs, because the "sky light" emitting from one block of glowstone will be "saved" as "sky light" in nearby blocks, so they must all be broken before you can replace them or else it'll still think there's skylight around.
Confirmed for 1.9-pre1, although glowstone doesn't seem to be affected anymore. It still occurs with water and cobwebs.
Please mark both videos (https://youtu.be/bPUdssOvU78 and http://youtu.be/8nTd1KbbrLA) as either public or hidden, if it's private, we can't watch them.
Confirmed for 1.10, glowstone not affected. You can see the result with cobweb on this video : https://youtu.be/fZa-kKz-K3E
What i think is that when the ceiling is sealed, all the air blocks's light level underneath are updated but they omit other blocks (for optimisation purpose) so cobweb is not updated except if you place the block just above it (for glass and other stuff it works though)
F3 confirms that the light is skylight, not block light
Confirmed for 1.12.1
@unknown, 1.12.1 has already been marked as affected.
Redstone ore is supposed to do this, according to Minecraft.net here. However, this may be wrong, because I doubt the author would know definitively what the desired behavior should be here.

No, it's a bug and the blog author was already notified.
Can confirm.