So I'm still having this issue. I'm somewhat giving up here until someone has a better idea of what to do.
Issue: I can't iMessage the majority of people. I can, however iMessage two contacts. There are some contacts that simply say SMS (ie, iMessage isn't even an option anymore for them) and some where iMessage fail. iMessage is enabled on the phone and doesn't have an activation issue. Everything *seems* fine. This is an iPhone 6 on Verizon (my first Verizon phone).
I've done all the following today (Saturday, March 14th) when Apple says they are experiencing zero server issues:
1) I've tried hard rebooting the phone.
2) I've tried Network Reset with iMessage enabled, followed by a hard reboot
3) I've disabled iMessage, done another network reset, followed by a hard reboot, then turned iMessage back on
4) I've tried deleting iMessage history of someone's and start a new conversation with them
I'm getting iMessages on my Macbook Pro. If I SMS someone from my Macbook Pro, it shows up on my phone (Continuity is working). I updated over WiFi
So the only thing I can possibly think would separate me from all the people who updated just fine:
1) iPhone 6
2) Verizon phone
3) Continuity is configured
I'm going to try a Restore, but I'm not optimistic.