Depends.
In class sparring - Not unless I'm told to.
Animal day - Head-gear, Groin-guard, Mouth-guard, Shin-pads, Bracer-pads, Gloves, Torso-shield.
Kyokushin competition (all open) - Mouth-guard, sometimes wrist wraps (Groin-guard is optional, I prefer to take my chances)
Open Karate competitions - Gloves, Booties, Mouth-guard, Groin-guard, Head-gear.
Open TKD competitions - Gloves, Booties, Chest and Back-guard, Mouth-guard, Groin-guard, Head-gear.
Muay Thai competitions - Gloves, Shin-pads, Mouth-guard, Groin-guard.
Kickboxing - Gloves, Shin and instep pads, Mouth-guard, Groin-guard, Head-gear.
MMA - Mouth-guard and Gloves (Groin-guard depends on competition) I sometimes wear a knee-pad on my right knee, it gets twitchy when it gets mat burn.