Several iOS 10 apps enable typing suggestions by default, even if these were disabled prior to iOS 10. This is especially notable in Messages, where the suggestions include emoji.
How do I disable typing suggestions in iOS 10?
Tap and hold the language key (the one that looks like a globe or possibly an Emoji smile face) and set the toggle for "Predictive" to off.
If, like mine you do not get the option to change the keyboard on your messages app. Go to Settings > General > Keyboard > Predictive. Here you can switch it off.
The problem with this is that it also seems to shut off autocorrect and predictive text within the text bar -- I want nothing to do with the suggested words that can be tapped, but I like the autocorrect and suggestions that hover while typing. If that makes sense.
Update: Actually, this only seems to happen when turning off predictive text within the settings app. So this is good.