Paper or Plastic?

Plastic lends itself perfectly to beach bags--for holding wet clothes and towels and sand that can later just be hosed clean.
So one option is to consider knitting or crocheting from 'yarn' cut from plastic grocery bags.

I have lots of links on the sidebar here, including some great ideas from Marlo's Crochet Corner.

Still need inspiration? How about this:

Alexis Berger creates some amazing designs by crocheting plastic bags. You can view her public gallery via her Picassa web album.

Or, if you don't want to work with plastic, you can consider unusual materials.
Make a burlap beach bag from Craftown.

Or how about duct tape?!
Here's how at Making Friends.