I'll never use them (with the exception of the times I send "Happy birthday" and iMessage automatically adds the balloon effects, but I can't remember if that actually shows up on my phone or not). I can't control what people *send to me*, however. I want to turn off effects for messages that people try to send me, specifically. I just don't care or want to see them.
I find them quite annoying! If you turn On the reduce motion option in accessibility, it will turn off the animations.
How Do I Turn Off Messages Effects On My iPhone, iPad, or iPod?
Open Settings.
Tap on General.
Tap on Accessibility.
Tap on Reduce Motion.
Tap the switch on the right side of Reduce Motion to turn it on and disable iMessage effects in the Messages app on your iPhone, iPad, or iPod.
Update: with newest version of 10, you can turn off just the imessage effect- there is a new option- Step #5. Finally, turn off the switch next to “Auto-Play Message Effects.”
Turn off the switch next to “Auto-Play Message Effects.”