How can I prevent my alarm from going off when my phone is on silent or turned off?

This has happened a few times to me, I'll have my phone on silent or turned off, but the alarm still goes off (iPhone 3GS).

I have a few alarms set throughout the day to remind me to do daily things (take my pill, etc...). Well, one of these alarms went off while I was in a local theater watching a play, even though my phone was set to silent. The actors even noticed it. SOOOO embarrassing...

How can I stop this from happening? Are there any apps that work the same as the alarm but don't sound when your phone is on silent?

It makes perfect sense that the alarm still works because more people use their phones as alarms these days. But they don't want to be awakened in the middle of the night by a text or phone call (I'm one of these people).

You could turn your phone off completely. Or open the clock app and turn that particular alarm off.
No alarm apps I know of that don't sound when the phone is silenced.

I always just turn my alarm off. Easy as that.