I have a droid razr...but my other (original) droid had the same exact issue. My phone will call people all on it's own. My old droid did it all the time, my razr only does it when my alarm goes off and malfunctions (which is most of the time). My alarm will go off and only sound for about 2 seconds and quit...which is not good at all. When it stops my phone will call someone. It tried to call my Mom at 5 am one day and that is not good...she is 87 and would have got all worked up. I put a call blocker in and it somehow gets around it and calls people anyway. Any suggestions? I know a working alarm would be VERY nice....sigh. I love my Motorola's but this makes me never want to buy one again......
My guess (since you have had two different phones with the same problem) is an app that you have downloaded is interferring with the basic operation of your phone. First clear the cache on your phone. If still auto-dialing, then run your phone in Safe Mode for a day or two to see if the problem goes away. If no problem while running in Safe Mode then it's a safe bet that an app is not playing nice. Either remove all of your apps and add them back one at a time until the offending app is found or remove them one at a time until the problem goes away. As a last resort do a factory reset.
If you don't know how to do them, do a search for Razr Safe Mode, cache clear, and factory reset; there are many reference in this forum and Google.
I definitely know how important it is to have a working alarm on your phone. I use the alarm on my phone every day to get up for work. I'd be lost without it!
@breezex provided a great suggestion. Did you try clearing the application cache http://vz.to/Ljt4tF? You can also try clearing the temporay internet files as well http://vz.to/17g7dOV. Since this also happen on your other phone it may be a 3rd party apps on the phone causing the issue.
If the issue persist after the steps above, run the phone is safe mode http://vz.to/rxg0ii for a day and see if the issue stops.
Keep me posted.
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Do you use a non-OEM charger? Does this only happen when the phone is charging? I know both my Droid and Droid RAZR make calls and go crazy when I use after market chargers.