Something I don't ever see on anyone's hospital bag list -
Pack a notebook and pen! I had one for both visits to L&D, and any stats or progress I had were recorded into that book. It's always been kind of cool to see the updates and how fast I dilated. I also wrote down comments nurses and my OB made during the process. Looking back I still can't believe how fast I went from 4 cm to 10, or how long I was actually pushing for. It seemed like a lot longer than what it actually was!
And the best thing to bring home from the hospital (besides the baby, lol) is that peri-squirt bottle your nurse will give you. It's so much easier to use than a sitz bath, and I totally attribute how fast I healed to using it whenever I wanted to clean up after using the bathroom. Warm water in that thing was so soothing!