Just thought I would add my two cents ...
I got the new samsung galaxy note 3 and have had the same issues over the past week.
I tried the following solutions:
1. Turned off iMessages on old phone
2. Deactivated my iPhone from apple accounts
3. Deactivated my iPhone from iCloud
4. Deactivated my iPhone from iTunes
5. Changed my apple account password
None of the above worked by themselves but may have helped contribute to the final solution.
I finally spoke with an apple senior technition at length, and they were able to confirm that iMessages had been turned off on my old iPhone. Thus, the problem now was only with those wanting to text me who had (1) texted me in the past, and (2) had apple accounts. Once the iMessage feature on my old phone was confirmed to be off, they would receive an error message when trying to text me.
The technition advised me that at this point the following needs to happen: these people need to delete our text conversation history and then turn their phone on and off. At that point, their phone would no longer automatically send iMessages, but would send the messages as SMS.
AND THIS WORKED.
Incredibly frustrating to have to notify everyone that has ever texted me from an iDevice that they have to take these steps. But at least there is a solution.
Good luck to you all!