Surprised noone posted this simple and compact day counter:
What you'll need: 2 Chests, 1 Redstone dust, 1 Daylight sensor, 1 Hopper, whatever leftover dirt or cobble you have crowding your chests from mining.
Place the 2 chests as a double chest.
Connect a hopper to the double chest (Do this by shift-clicking the double chest with a hopper in hand).
Connect the hopper to the daylight sensor by using the redstone dust.
Put the dirt and cobblestone into the hopper.
How it works: When its daytime the daylight sensor activates the hopper which dispenses one cobblestone or dirt into the chest. During nighttime it shuts off and the next day another block goes into the chest.
Then after a few days/hours of playing minecraft look into the chest. Each block in the chest = 1 minecraft day.