I normally bring my APK drawstring with water, athletic tape (for rips), newskin (for anything that bleeds), alcohol wipes (for disinfecting), an ice pack (one of the crack and shake kinds), some money for food or a banana, cell phone, and a bandana (for drying off rails, or wrapping up busted ankles).
It's not that I'm accident prone.. it's that I'm an EMT. The go-to girl at jams for pain fixage. So, I like to be prepared. A splash of newskin can turn a jam-ending rip into a watertight, train-on-able minor nuisance. Ice works best when applied immediately after an injury, so I like to keep those ice packs right at hand. It can mean the difference between feeling better in a few days to feeling better in a few hours.
I highly suggest slipping a tiny first aid kit into all of your training bags. Immensely useful!