Many of the older phones, (I know Black Berries were this way) had alarms that would work with the "power off". In reality the phone was not actually off, it was in more like a deep sleep, the only way to power them down 100% was to pull the battery.
With the new smart phones when you power them down they are actually off. So you will not be able to find an alarm that works with the phone off.
If your worried about data or battery use, you can switch on airplane mode and put your battery mode on nighttime saver.
Hope this helps.
I am in the UK and have recently got an HTC Wildfire with Android 2.2.
I had a "simple" Samsung (Absolutely no disrespect) that worked perfectley. I used it as an alarm clock and the alarm came on when the phone was switched off. I have gone through the Market and looked at several apps but not found any that would set the alarm off when the phone is not switched on and I miss that. It seems such a waste to have to have to phone switched on all night just to get the alarm to work in the morning,
Any ideas anyone ?