Because it is simply impractical to carry a comprehensive first aid kit you will almost surely have to improvise for anything worse than a minor boo boo.
A cell phone to call emergency services is probably the best thing most of us can do for a more serious injury/accident. For very rural commuters or Mt. bikers you may be on your own for awhile or have to limp out to somewhere you can be found. In that case a bit more first and/or second aid may be in order.

I carry about a dozen paper towels in a ziplock sandwich bag in my tool pouch. These can be used to wipe greasy hands or cover a wound. The baggie can also be used in a pinch to valve a sucking chest wound.
I also carry a spare tube in another baggy wrapped in a large bandanna with a rubber band(to protect the tube from damage) that can be used for a pressure bandage/ constriction band ect for larger wounds or unexpected amputations. (NEVER apply a constriction band or tourniquet unless you have been trained to do so) The large bandanna can be used to make a sling or battle type dressing, pack a very large wound ect.
Water bottle for emergency eye wash/ wound flushing.
Splinting is probably best left to EMS but a Mt. biker may find the need to splint. A tire pump can easily be extended to just the right length to splint an arm or lower leg.
Learn CPR and take a first aid class. There is not much worse than watching someones life slip away before your very eyes and not being able to do a darn thing about it. ( you will have nightmares for the rest of your life ) Knowing first/second aid can make the difference in a lot of situations but you have to also accept your limitations.