I have a replacement Motorola Droid (actually my 3rd one now). I have an ap that was not downloaded from the Market, but was developed internally. Is there any way to save the ap to my SD card and transfer it to my replacement phone? The rest of the aps transferred through my Google account backup.
MyBackup (https://market.android.com/details?id=com.rerware.android.MyBackupPro&feature=search_result) app does this well and you can also use Astro (https://market.android.com/details?id=com.metago.astro&feature=search_result) or ES file explorer (https://market.android.com/details?id=com.estrongs.android.pop&feature=search_result) that has a option to backup apps.
But keep in mind when you side load apps from a sd card usually does not show as being installed through the market so you wont get updates usually and also apps that require license keys to use full versions will not work fully until you add key back in.
i'm not very techy....so maybe anyone else has some input here...but you mention you are on your 3rd droid? are you sure that some of these apps aren't the problem? if you're device keeps crashing, i'm just wondering if you're putting the same bad app or bad sd card in the new device which could be causing the issue???
I have two Droid X... One for use and one for testing and the apps that I suggested works without any issues to device. If you want the simplies way then MyBackup would be your solution. All you have to do is select the option you want from a very simple interface.
Also it isnt wise to allow the Auto restore option in Droid X to place apps back on your device because it has a history of starting issues...