What caused my TNT Minecarts to explode?
Solution 1:
It would appear that if 2 TNT minecarts run into each other on a curve with sufficient speed, it will set them off.
Step 1: Build a loop.
Step 2: See if Minecarts explode when place next to each other.
Nope, looks like this is safe.
Step 3: See if Minecarts explode when across from each other.
Nope, this seems fine too.
Step 4: Try to make minecarts explode on straight sections.
This never set it off (this picture is different because I tried many times to figure out where it was exploding).
Step 5: Make minecarts crash on a curve.
Ah ha! This resulted in an explosion.
This did not happen every time the minecarts collided in the corner, so this seems to be somewhat randomly caused.
Further Science
Does it need to be 2 TNT carts?
No! In fact, regular Minecarts seemed to set off the TNT more frequently.
Also, chickens are friends, not food fireworks.