There are many types of reflexes: Tendon reflexes, eye reflexes, eye-lid reflexes, face reflexes. Reflexes that help us to flinch. Reflexes that keep us from falling when we trip. Even babies have their own set of reflexes.
This might shock you, but I am an anatomical anomaly. I have more reflexes than other people. Here are a few of them:
Hit-side-of-garage-with-rear-view-mirror reflex (This one PLAGUES me!)
Kick-husband-when-child-cries-at-night reflex (It is instantaneous!)
Now, they haven't been documented yet, but I am convinced that these must be reflexes, because while they are happening, I am definitely not using my brain.