I'm surprised no one has mentioned old school foam sleeping pads (ensolite or similar). These are one of the best items for improvised first aid.

The "jelly roll splint" is a classic for a leg injury: Take two pads, put them cross ways under the injured leg. Adjust the overlap of the pads to get the proper length for the leg. For patient comfort it is usually best to put a small wad of clothing under the knee so it is flexed slightly. Start from both sides and roll the ends of the pads towards the leg. The idea is to end up with the leg cradled between two rolls of pad. Then secure with cravats, webbing, or whatever. This has been used successfully many times for everything from a blown knee to a full on leg fracture. It is comfortable for the patient, and provides padding and insulation, and it is easy to monitor the leg for swelling.

A single pad can be used for a shorter splint. Or the pad can be cut up to make a reasonably good C-collar. Or can be cut to provide padding inside some other splint. Or used as padding in a rigid stokes type litter. Or....other uses are limited only by your creativity.

Note that more modern inflatable sleeping pads don't work very well in this application. Although I carry an inflatable pad for sleeping, I also almost always have a foam pad along as well.

One of the best uses I've seen was when I was once backpacking in the Talkeetna Mountains, and met a NOLS group with an injured woman. NOLS does very long backpacks in that area, stopping at isolated lakes for resupply by floatplane. The woman had blown out her knee. Rather than calling for imediate extraction, the group had splinted her leg with a jelly roll, adjusted slightly loose so she had some flex in the knee, and could still hike, albeit slowly. They distributed her gear to the rest of the group, and were slowly making their way to the next resupply point, where the woman could be evacuated. A great example of self sufficiency and self rescue, in my opinion.