10L Axle
This is a result of overloading with excessive torque. I don't remember how this happened exactly, but I have a few axles that have plastically deformed due to too much torque.

1x1 Plates and Tiles
The translucent 1x1 plates and tiles are quite susceptible to cracking and splitting down the middle. This just seemed to happen after some "normal" use.

24t & 8t Gears
A common injury among gears due to excessive torque. I should have noted the reduction ratio at failure for the 8t. The 24t gear failed at a 1:648 ratio driven by a 4.5volt motor.

2x8 Plate
I dunno. I guess I was hungry.

4.5 volt Connector
This is common with the 4.5 volt motor plug connectors. (And I guess 12 volt too- but I never owned any of those)

Blown Out Arm (Minifig)
I don't remember how this happened, but the arm will not hold a minifig hand anymore.

Half Peg (Technic)
Pliers, I think. Or maybe I just got hungry again. You'd think I would learn that ABS doesn't taste very good.

Helmet (Minifig)
A common breakage among the old style minifig helmets was that the chin gaurd would crack in the middle. If pressed further, the whole chin gaurd would fail.

I Wanted Green
Oops. I was a stupid kid! Long, long ago, In a bedroom far, far away...  I WANTED GREEN BRICKS!

Old Pneumatic Cylinder
I suspect this is probably common amongst the old Technic pneumatic cylinders as the shaft was made of plastic. The new yellow cylinders are metal and have not failed on me as this one had.

Robot Arm
Common injury.

Technic 1x6 Plate
Many of my 1x4, 1x6, 1x8, and 1x10 Technic plates with holes have failed in this manner. The end breaks off easily because it has "teeth" (i.e. reduced section- not as strong as a solid piece).

Technic 2x? Plate
Oops again! I don't remember this one, but it was surely due to excessive force on my part.

Technic Beams
This is common amongst old used beams. Fatigue cracks appear about mid-span on the bottoms and if pressed further, the cracks will propagate and snap the beam in two.

Window Frame
I have several with the shutter-holder tabs broken off. I guess this happened when I used to keep all my pieces in one huge box and everything got squashed.