I've only stopped 3 times in my time as an EMT. Once was b/c I heard the call dispatched and it was literally less than a quarter mile down the road that I was on and it was in my way. lol. I was the first "responder" on scene and assessed the situation and held c-spine until the FD arrived. The patient was riding her bike and was hit by a car. No helmet. I had 2 RN's at the scene and they were basically worthless, I asked one of them to get me a pulse so that I have something to tell the medic when it arrived and she just stared at me like I was from Mars. :?
The second time I stopped was when I was at the beach and a few cars in front of me, someone had t-boned a motorcyclist and he flipped over the handle bars. Once again I just told him to lay still, I left his helmet on, had my buddy hold c-spine and I got a set of vitals and did a quick trauma assessment as the medic rolled up.
The third time was I just stopped one night b/c someone had hit a deer and it was in the middle of the slow lane quivering. I stopped and blocked the lane off and waited for PD to arrive and terminate it.
I won't stop if there is already emergency equipment on scene. In my car, I only have some gloves and a very basic first aid kit.