Windmagic does make a good point. Don't ship out with pre-existing conditions that cannot be handled, or stabilized, afloat.
CD makes excellent points.
One of my duties on board ship was medical officer. We took a month long course that was basically advanced EMT. Never needed the serious stuff, although I sailed with a fellow who helped deliver six babies in three days! His ship was involved in the evac. of Viet Nam.
Unfortunately, in a serious accident, you are not going to have what you need. You will be more likely to need morphine than you will anti-biotics, you guess which one you can't get. Infection takes time-that's antibiotics. Serious trauma/serious pain is instantaneous-that's morphine.
Many things mentioned, like the jock itch cream, are very good. Some of the most common things I would think of include: all manner of treatment for every level of burns. Burns are probably the frequent injury-they happen in myriad ways and are always unexpected. Scalding water to the foot can disable the heartiest soul. In addition to numerous pre-packaged dressings, I would recommend getting a big jar of Silvadene cream. It is prescription, but your physician should be willing given your intended use. This stuff is the Poly-glo of burn treatment, everything from severe sunburn up to third-degree. It relieves the pain and greatly aids in healing. Get as big a tub as you can. Ask anyone who has ever been burned about the white cream they got from the Dr.
Touniquet material and air splints are essentials. We're not going to be Marcus Welby-all we are trying to do is stabilise the patients condition.
If you have a nursing friend, perhaps you can talk them into showing you how to start an IV. In my class, we practised on each other! It's really not hard to get the knack of it. If you have that skill, it is worthwhile to carry Ringer's lactate, and other IV administered fluids. In severe trauma/sickness simply getting a dextrose solution into the blood stream can be invaluable.
The most used things will be items that you commonly use ashore and take most for granted. If you are incapacitated in the head with severe diarrhea, you can't sail the vessel. Upset stomaches, migraines, tooth-ache-all are things quite easily dealt with ashore that can be debilitating at sea. Plan heavily on these. Just for diarrhea I'd take multiple products-sometimes one works better than another. In addition to good old aspirin, I recommend ibuprofen. In addition to being a pain reliever, it is an anti-inflammatory and muscle relaxant. Ingested in Motrin strength it works wonders on that geeked back, cracked rib, or pulled muscle.
If you take a medication regularly I would recommend that you save the pill bottles and split up the amount you are taking with you. If you have only the one bottle and it's contents inadvertently get soaked, dropped over-board, or in the bilge-you have options. The medical bag is not a bad place for a spare set of contacts or glasses also.
If you don't carry scalpels, through an exacto-knife in the kit with different size blades. They work wonders on splinters, boils, and such.
As has probably been mentioned, most of the kits I've seen start out with good ideas but fall short. A bunch of dinky band-aids are useless when you need a big one-and your kit gave you six! Dump the dinky ones, buy a big 'ol box of the big ones and cut 'em if you need to. Guaze is another one-can't have enough-especially "cling" that sticks to itself. The trouble with the kits is that you get an "initial" amount of what you need, with nothing for tomorrow. If you get burned, you're going to need to treat it for the duration-figure on a chest or back-sized burn and the amount of cream and guaze you'd need for the duration. Betcha it's alot more than you thought.
As wind magic says, don't get hurt or sick. It's much easier to avoid both than it is to treat either. Plan ahead and be safe in your practises.