I'm only posting this because it took me forever to get this done and the way to do it is so convoluted and frustrating. I have a iPhone 4s running iOS 6.1.3 and I just did this after several weeks of research.
Tomhr260's instructions are pretty much spot on. I've recopied them here, but changed it a bit to make more sense (at least in my mind).
1) Backup iPhone/iPod/iPad to iTunes. Sync your iPhone/iPod/iPad and make sure the backup is help locally.
2) Close iTunes but leave your device plugged in to your computer
3) Download iBackupBot
4) Open iBackupBot
5) Select your backup from the left column. For me, it was the last one with today's date on it.
6) Navigate to "Library/Preferences/com.apple.springboard.plist" (there may be two files named this; try them both) and double-click to open.
This was the hardest part. There are actually two files that are com.apple.springboard.plist. You want the one here:
System Files/HomeDomain/Library/Preferences/com.apple.springboard.plist
Double click the file to open it. The whole "This is a TRIAL Version" will appear. You do NOT need to buy the program. Just hit cancel and the file will open.
7) If the backup is from iOS 4.X or lower then you should be able to find "<key>SBParentalControlsPIN</key>" somewhere in this file and your passcode will be below this line.
If your backup is iOS 5 or higher, then continue on. I assume everyone is running iOS 6 or higher so continue.
8) Look for and change the string for "SBParentalControlsFailedAttempts" to 0.
Here is where things get a little complicated. For some reason, I was not able to make any changes that got saved to the .plist file. I did it numerous times and nothing happened. In summary, what I did was export the .plist file, and use another program to make the changes, then reimported it using iBackupBot and then restored it to the iphone. Instructions continue below:
8a) So you have the com.apple.springboard.plist open. Go to the icons on top and click Export. Pick a destination (I used the Desktop).
8b) Download PlistEditPro to edit the .plist document (http://www.macupdate.com/app/mac/14363/plistedit-pro). After you download and install the PlistEditPro, you can right-click the com.apple.springboard.plist file and Open With PlistEditPro.
8c) If you don't see the commands, or if it says "The property list is in binary format and has no textual representation. To see a textual representation, choose a different property list format using the Change Format submenu located in the Operations menu." then go to the Operations Menu, click Format and select XML. That should show the commands.
8d) Look for (about 2/3 down) and change the string for "SBParentalControlsFailedAttempts" to 1. I did this rather than 0 in case there wasn't supposed to be anything if there were 0 failed attempts and I didn't want to screw it up.
9) Directly below the FailedAttempts, you will see:
<dict>
<key>countryCode</key>
<string>us</string>
</dict>"
After THAT, add this text:
<key>SBParentalControlsPIN</key>
<string>1234</string>
Make sure it matches the rest of the file. You will need to remove leading spaces for each command line and it should be tabbed over.
10) Click save. If you get an error, then you probably have extra spaces or tabs in there. Go back and make it consistent. Click save.
11) Close out of that file
11a) Go back to iBackupBot. Click Import on the top and select the just edited com.apple.springboard.plist file.
12) Click restore backup/file to iPhone/iPod Touch (the icon of an iPhone and a blue arrow) located under the menu bar in iBackupBot
13) After restore is done (should be like 10 seconds) and phone restarts the password should be 1234.
14) Change it to something you will remember this time.
Hope this helps someone else. I know it's super frustrating and I don't know why the password reset can't be done to via an email or phone call or whatever, but here it is and it works.