When you choose the sound for a new alarm that you are creating in the Clock application of iOS, I used to quickly select the back button to silence the sound since it always plays a preview of it. This is especially important if you have a significant other sleeping right next to you. However this still will play the sound for about half a second or so, but there is an easy work-around.

Simply double tap the alarm sound you are choosing rather than single tap. Double tapping the tone of choice will select it but not play the audio at all.

[crarko adds: It does indeed work.]