What happens to a vehicle if you simply start to ignore your oil change indicator?

This is how an Audi VR6 engine cylinder head (cover removed) looks when new:

This is how it looks when used and properly maintained:

And this is how it looks after being driven 135,000km (84,000mi) with the same oil:

If a nugget of that gunk comes loose in the wrong place, it clogs an oil channel and kills the engine.

The gunk also acts as an insulator, constantly overheating parts of the engine, leading to warping and cracking.

Motor oil acts as a lubricant between the fast moving metal parts of an engine. In the first few days, probably nothing will happen, as there still is oil circulating throughout the engine. As the oil degrades, it will not do its job as efficiently, and metal parts may rub against each other briefly. Further degradation results in the oils consistency being affected so much that it is unable to lubricate the metal parts AT ALL. Heat builds up, piston heads start to melt, connecting rods become undone, the crankshaft seizes, valves start to melt, ending with the engine grinding to a literal screeching halt. Ive seen engines actually explode and catch fire.

Lesson: CHANGE YOUR OIL!