Auditions are job interviews. Plain and simple. You walk into a job interview or a an audition room you are looking across that desk and thinking you have to knock the socks off of this guy or else you'll never be back in this building again. There's a thing about being memorable that can be a double edged sword. You can either do it in the way that someone will tell a story about you for the rest of their life kind of way or in the way that you do something so well that they have to see you again.
I prefer the latter and I try and do this in a number of ways following a set of three P's.
Preparation is very key. There's a lot of ways to do this, as Michael mentioned, like picking a monologue that would translate over to a character in a show that is being cast. The main thing I harp on is be prepared with your materials at a minute's notice. What if you met Quentin Tarantino on the street and he asked you to do a comedic monologue, could you do it? You should.
I am constantly updating a book of monologues and songs that I have memorized and can do at the drop of a hat. My goal is to have twelve monologues and six songs memorized at all times, but if you really skim it down it's six monologues and two songs. Two Shakespeare comedic/dramatic, two classical comedic/dramatic and two modern comedic dramatic should be available to you any time as well as a ballad and an upbeat song if you're a singer. This may seem like overkill, but I know I've had auditions where I've been able to give people options to choose from or something else to follow up an audition that made me seem much more desirable in the long run.
Professionalism is the very first thing on my mind when I actually get into a room. Don't show up in jeans and a t-shirt unless you're trying out for Grease. The rule for job interviews is dress one step above the normal required dress code, so why shouldn't that apply to an audition. It shows you have dedication to your craft and you take this seriously. Be on time, hhake hands, be polite to everyone involved including the front room check in person and always say thank you. These people want to enter into a business deal with you and you should respect that side of the business.
The last thing that tops it all off is Personality. There's no reason you can't crack a joke or talk to someone in the room about the show. These people want to enter into a business contract, yes, but actor's are social creatures and they want to make sure you're not a dick either. DOn't waste someone's time with talk if they just want a reading, but I've always made comments on something I read about the theatre or if someone was wearing a University of Wisconsin shirt I will always say "Go Badgers" to them.
If you can combine all of these things and do them well, there is no reason you shouldn't be remembered just for the sure tact and skill you show in your audition. Be memorable without the gimmicks and be remembered because you are so good at your craft that someone can't afford not to have you.