If we get there first, we bring our jump bag (which has everything in it that the ambulance has in the back, just not so many of each item- which includes but is not limited to intubation kit, airway "stuff", bleeding control, BP cuffs, IV kit, drugs, etc.), and our Phillips monitor (rock on with the on-screen 12-Lead!). And of course our stretcher, which has frame mounted O2, a sheet on it, an extra sheet for modesty or cold pt, and occassionally a towel and blanket. Suction also comes with us for Cardiac Arrest. Backboards and C-Collars as necessary, often brought as precaution in the high rises. We do not carry our clipboards, but every jump bag has AMA forms in the back, as they are the only form you need on scene, if any.
If fire gets there first, we just bring our stretcher. Unless the building is greater than three stories and we are running with an engine or truck (as opposed to a rescue), per protocol we have to bring all our gear. Somedays the engines are ALS engines, somedays only ILS.
Of course there are times when specialized equipment is brought in. For pediatrics, we have a Peds ALS jump kit. Same as the regular one, just with Ped-sized equipment. If it's a imminent birth we also bring in an OB kit incase we have to deliver on scene.
Really the only thing I've ever had to go back to the truck for was backboards. And often its because it wasn't a traumatic call, it's just being used for patient movement.
Oh, and we are to go nowhere without our portable radios. They have a button on them called a "Code 5" button. When pressed, it sets off an alarm in our dispatch, in AMR's dispatch, and in FAO's dispatch (I think). Your radio ID also comes across a monitor in the dispatch. Code 5 here in Las Vegas means there is a danger to your life and assistance is needed immediately. When you press the button, dispatch will come over the radio and ask if you are "Code 4" which means everything is okay, there are no threats. If no response, they will ask again and for a location and further information. If no response still, they will just track you with our AVL's. You will get two ambulances (from either agency), a supervisor from your agency, fire and Metro (our PD). Fortunately this doesn't have to be used very often, but occassionally it does. A few weeks back one of our crews was shot at. I am glad they have a system in place for it!