HERE'S WHAT WORKED FOR ME! -- I switched from an iPhone 4 to a Galaxy 4S. My old iPhone has a CDMA (has no sim card) -- so the "wipe the sim card" was not an option for me, as some had suggested online. I don't even think that woulda helped.
Hubby still has an iPhone, and his messages usually would not go through, or only after a delay, because despite removing my info from his address book & cloud, his phone still seemed to "remember" me as an iPhone user and thus was always trying to iMessage when texting me. I was able to get his phone to stop doing that simply unchecking his "iMessage" option under settings/messages on his phone, but I can't ask all my friends to do that just to connect with my phone (if they don't have unlimited texting on their plans, that could cost them money!). So I kept reading online, did everything I could, hours and hours... and was ready to surrender to the big bad monopolizer (i.e. become a conformist, return my droid, and settle for an iPhone). But -- grrrrr!! I really like my new droid!
SO -- I read somewhere that even if you have disassociated your iPhone from Apple/cloud account, your email address that's associated with your apple account may still be causing people's phones to identify your contact/account as an iPhone (if they have your e-mail address in their contacts). So, CHANGE YOUR APPLE ACCOUNT IDENTITY and don't let your public e-mail addresses be linked with your Apple account. My apple identity log-in was my gmail address, so I changed it to a junk e-mail account that I never use and no one knows. As soon as I did that, I turned the "iMessage" option back ON on hubby's phone, sent myself a message from his phone, and it did NOT turn blue on his screen (newbies: the dreaded blue means someone's iPhone thinks your phone number is an iPhone too and therefore tries to send texts as iMessages.)
Now, if I find that other people's phones are still not reaching me (especially people with iPhones with whom I text a lot) I will update this post. But for now I am quite proud of myself.
It's possible people will still need to go into their contacts and make sure your phone number is not labeled as an iPhone -- which I had already done on hubby's phone (that had not helped). They may even just want to REMOVE their contact information for you, for good measure, and re-type it in. But that's still less troublesome for them than asking them to turn off their phone's ability to iMessage, just cuz you want to use a droid and want to receive their texts.
UPDATE: that did immediately work on hubby's phone, but on some friends' phones they still need to choose "send as sms" to get a text to me (even hubby's sometimes reverts back to iMessages when sending to my droid) -- BUT, more people are now having no problem sending to me, and some phones seem to be "learning" not to send as iMessage.