This question came to mind because I'll be working on a location set in a few days.
Many actors figure that as long as they have a fully-charged smart phone they really don't need anything else. That's not a bad idea, but having been on a lot of sets, there are a few other things I like to have.
I should mention here that I'm mostly talking about working in a principal role. For background work, besides bringing whatever wardrobe you'll need, a smart phone or possibly a tablet, are about the only things you will be able to have with you on the set - and remember, you will often have to leave anything bigger than a phone behind when you are actually shooting.
Principals are able to bring more because we usually have our own little room in a trailer (called a "Honey-wagon"), and can leave our stuff in there when we are shooting. The room will often contain a DVD player and I'll usually throw one or two DVDs in my bag to watch. This is because I've been on too many sets where my scene shoots 6 hours after my call time. This is especially true with "day player' roles where you are only doing one scene out of the whole day - so, you can end up spending a lot of time hanging out in your trailer, waiting.
I'll also bring a book. Either on a tablet or a hard copy. And of course plenty of good music. One of the tricks to getting your energy up quickly after sitting on your butt for a few hours, is to be able to throw on an upbeat song or two when the 2nd A.D. tells you that you'll be on the set in ten minutes.
And although there's usually plenty of munchies at the craft services table, if there's something you like to snack on that's a little different (sunflower seeds, dried fruit, etc.), you might want to bring that with you. I've seen more than a few craft services tables with a few pieces of fruit and a huge amount of candy and cookies. So, if sugar isn't your thing, bring your own snack.
And that's about it. It's all about keeping busy in a low-key way. Because it's exciting to be on the set, newer actors will often spend a lot of time wandering around, unable to sit and relax for long periods. But that can really burn you out on a long shoot, so the trick is to be able to relax your body, but keep your mind somewhat simulated.