I carry a kit for the group. My group mainly consists of boy scouts. Because boy scouts are accident prone, and I want to stay away from law suits because I didn't carry something, my kit is probably bigger than most here. Of course, it is smaller than a lot of other kits with the same purpose.

When I hike alone or with my kids, a quart freezer bag does the trick. If you want to go heavier duty, try an Aloksak.

As for something heavy duty, this is what I use to carry my group kit in. Rip away EMT pouch
They also make a smaller one.
small rip away pouch
Here is a review I did on the pouch.
pouch review
And here is a description of its contents.
first aid kit
I built this kit for backpacking with scouts, but have pretty much taken it everywhere else we go over the last year+.