This is what I've collected over the years. Some of it is more useful for other livestock, though. Things in bold are must haves IMO. You can treat nearly anything with just those few things.
Stethoscope
Nutridrench
Clear iodine
Betadine
Aspirin
Saline packets
Save a chick electrolytes
Save a chick probiotics
Waxelene (for scaly leg mites)
Q tips/cotton balls
Bandage tape
Triple antibiotic ointment
Preparation H, for prolapsed vents
Styptic powder
Vetericyn
Gauze pads
Vetwrap
Syringes in different sizes
Amoxicillin
Corid
Worming meds
Pipe cutters... for when the rest is not enough.
EDIT: potato chip's post reminded me; I also have bandage scissors, pointed scissors, a small razor blade, and tweezers.