While Katy Perry (well, BebopVox to be exact) does have a certain view, I wonder if the day/night cycle affects anything underground? Spawn rates, mob movements, mob hostility, etc?
The only thing that is affected underground is that at night you will have less mobs because they will be spawning above ground,
In single player the caps are as follows
Hostile = 79
Passive = 11
Ambient = 16
Water = 5
so at night say 20 mobs are spawned above ground that means that only 59 could spawn below and that is in all current cave networks that are loaded underground (chunks loaded)
The cap is checked once at the beginning of each spawning cycle. If the number of living mobs in a category is over its cap, the entire spawning cycle for that category is skipped.
This means that it is safer to mine at night. as there is the possibilty of more mobs underground during the day where it could reach the full cap.
Another win for the clock item
Additionally to note is that if a hostile mob has had no player with 32 blocks of it for more than 30 seconds then it has a 1/800 chance of despawning Per spawncheckcycle. and those are every 5 ticks, this applies to Y distance so the deeper underground you get the less mobs on the surface.
Also if you are more than 128 blocks of a hostile mob it will immediately despawn
Note that this is a Euclidean sphere, not a cylinder from map top to bottom and not a taxicab sphere (which is more like an octahedron)
Also Mob behaviour
Spiders are hostile as long as the light level immediately around them is 9 or less. If they are found in an area with a higher light level, they won't attack unless a player attacks first. Hostile spiders will continue to chase the player even if they are exposed to daytime or other well-lit locations. Conversely, a spider won't become hostile around a player when roaming in daylight, but if it wanders into a moderately shaded area (e.g. under a tree or rocky overhang) it will turn hostile and remain that way.
and then you have the obvious which is that zombies and skeletons will catch fire if they are in daylight.
No passive mobs are affected by the day/night cycle, their spawn rates and behaviour won't change during either. (wish the chickens would sleep so I could have peace and quiet)