Mefix tape or similar is awesome for making/securing medium and larger bandages. Especially when the patient needs to move, or it's for covering something more chronic like a large burn.
Essentialy it's a big roll of cloth that's like stretchy self-adhesive bandaid fabric, and you can cut it to any size you want. You can make little strips of it, or wrap a whole limb. Whatever you need.
Butterfly closures are also good. Two years ago Audrey sliped and smashed her chin on the bathtub and got a pressure cut on her chin that went down to the bone. It was only about 1/2" long, but really deep. I was home alone, giving all four girls a bath and had them naked and soapy, while I'm holding a screaming Audrey who's bleeding like a stuck pig all over me and the bathroom. :|
I called my father over to tend to the other girls. I though I'd have to go to the ER and traumatize her all over again with stitches, but keeping pressure on it, the bleeding stoped, with just this angry deep split in her chin looking at me. So I squeezed a little generic Neosporin in there, made sure the skin to either side was perfectly dry and not greasy, and threw a butterfly closure over it. And even with a 2 1/2 year old picking at it, it stayed on and it healed better than if she'd gotten stitches.