If you're playing -- and practicing -- hard enough to win, somebody could get hurt. If you're the coach or the team captain, are you ready for player injuries? Football injuries are more likely to occur in practice, but medical staff is usually only avaible on game days. The rest of the time, it's up to you. Baseball, tennis and basketball don't even have medical staff.
My favorite first aid kit is soap and water, but it's different on the field. You really do need a sports first aid kit filled with cold packs, antiseptic, wraps and lots of other stuff to handle the kinds of injuries that happen at sporting events.

Image courtesy of PriceGrabberThe 71-piece contents of this kit are meant to be used in sports situations. It has two instant cold packs, but if you make a habit of using these chemical packs, you'd better buy a case. I recommend using ice and saving these for when there's no other option. This relatively inexpensive sports first aid kit is good for peewee teams and elementary schools to carry out on the field.

Image courtesy of PriceGrabberThis kit is well-stocked and comes with a cell phone pocket. The shoulder strap can be turned into a belt to carry a cell phone. I like the idea for games and practices that don't have medical staff available. This first aid kit is not as large as the Mueller, but tends to run quite a bit cheaper.

Image courtesy of PriceGrabberAnother comprehensive trainer's first aid kit like the Mueller above. I haven't seen either of these sports first aid kits up close, but this one sounds like it may be a bit more versatile.

Image courtesy of PriceGrabberLike the feel of the Cramer bag but not the stuff? You can purchase the Cramer kit empty and fill it yourself. I always think the best first aid kits evolve over time. Once you identify the items you use the most, you can stock extras and leave out what you don't need. If you don't have anything, I recommend buying a fully stocked kit to start with then make it your own over time.

Image courtesy of PriceGrabberAnother basic sports first aid kit. Nothing fancy and priced reasonably enough for a coach or parent to buy out of pocket.