There are reasons why some people do well at auditions and most of the people who do are well prepared. And even before you go into an audition you should be fully prepared. So first of all you should...
1. Know Your Material
Auditions are nerve racking enough, so do yourself a favor and know what your auditioning with, whether it be a monologue, song or sides.
I know some people who like to listen to music before an audition. But I was at an audition once where a girl was asked to learn her callback song in 20 minutes in the waiting room and she borrowed my headphones to listen to it on Youtube. I just find they come in handy.
3. Water bottle
I don't know how to express how important water is. It is pretty essential and you should be drinking it all the time, but especially on days when you have an audition.
This is one of the most important things to have because it's the only visual of you the casting director and the rest of the creative team will have after you leave the room.
TIP: have a head shot on the front of your book so if you lose it people will know how to return it to you.
This is a list of everything you've done and all the training you've had. You want the creative team to know your experienced and depending on what you've done it shows the level your at.
TIP: Bring more than one, sometimes directors ask for that.
This is the material your auditioning with....so yeah it's pretty important.
7. A Snack
I find this helpful because an audition can be very long, callbacks can be longer. But if you are going to have a snack you should have something with out dairy and also you should try to have something that doesn't negatively affect your body. I usually have sushi because it doesn't affect my body in any way but every ones different, you should have what works for you.
8. A Bag
I have a bag I bring with me that contains hair ties, bobby pins, chap stick and gum. I also bring deodorant and perfume if I will be dancing, because sweat can be a killer.
9. Leotard and Tights
If your in a cut audition where you don't know when you'll be cut and you don't know if you'll be asked to dance, having dance cloths with you can be very useful to say the least. I really like Capezio cloths and dance shoes, they are really well made and durable.
These are very important for dance calls or callbacks. Usually you should bring all the shoes you have. Jazz shoes, ballet flats, character shoes and any other shoe you have. Also height is unfortunately a big part of casting. If your tall you shouldn't wear a heel because you don't want to be taller or the same size as your leading man. That's unfortunately the world your trying to work in. I'm 5'8, ballet flats are my best friend.
If you dance a lot in musicals you should get LaDucas, they're really good shoes.