The short answer is: Nothing that you wouldn't normally carry on your day-to-day person. Examples of generally appropriate props include cellphone, purse/wallet, pen/pencil, water/coffee/tea, housekeys, sunglasses/hat, book, etc...

But you must know that the minute you pull out a prop, you run the risk of appearing to lack the confidence to live in the empty vulnerable space of no props. To combat that assumption, you better justify and earn the choice to use it.

As always, there are exceptions to the appropriate props rule, but there is no exception to justifying and earning the use of props in an audition.

The other NO EXCEPTION rule is NEVER. BRING. A. WEAPON. TO. AN. AUDITION. (even if it is fake). Under no circumstances will it ever win you a role. And under most circumstances it will get you escorted out of the building and banned from ever returning, let alone ever auditioning for that casting office again.

3 ways in which a prop will help your audition

  1. Use a prop if it enhances the story. The prop should only be used in service to the storytelling. Don't let your prop overshadow the story. For instance if you are using your cellphone in a scene, 99.9% of the time your relationship with the person you're talking to is more important than your relationship with the phone itself. Make sure that you specify which LOVE relationship you are fighting for and play THAT CONFLICT rather than the trap - (eg. the phone that has terrible cell service).
  2. Build the props around YOU and your story. Not the other way around. You want the audience to remember the impact YOU bring to the stage. Remember, it is your job as an Actor to change the molecules in the room. A prop cannot change molecules, only a human being can. Only use a prop if it will endow you with Importance - in service of the text. Not the other way around.
  3. Get rid of your props as soon as possible. Props are to be used sparingly, specifically, and economically. Your auditioners want to see YOU! A prop will never be a substitute for the energy, choices, preparation, and commitment - aka Head + Heart + Hips that you bring. Let your props be an arrow in your quiver, but you need to rely on your craft to hit the bullseye.