Alice Fuji (Arachnid) has trained to use her mental disorder, Congenital Excessive Concentration, as a way to be aware of every detail and threat around her.
Having been blind since birth, Kaname Tousen (Bleach) trained his spiritual senses to give him deep awareness of his surroundings.
Jimmy Kudo/Conan Edogawa (Case Closed)
Super 17 (Dragon Ball GT) can automatically sense and processes every change in the air, sound, vibration, etc. in his surroundings, allowing him to predict Goku's Instant Transmission.
The Goblin Slayer (Goblin Slayer) is extremely alert of his surroundings...
...allowing him to detect goblins hiding in complete darkness.
Using their head sensors, Guyver Units (Guyver) can sense electromagnetic fields outside of their direct line of physical sight, allowing such feats as thermal imaging and the ability to hone in on sound waves and pick up on vibrations within the atmosphere.
Kars (JoJo's Bizarre Adventure Part II: Battle Tendency) can sense the body heat and air pressure of any living creature down to their exact weight and height.
With his mastery of Kenbunshoku/Observation Haki, Monkey D. Luffy (One Piece) is extremely alert to any and all danger around him.
With his mastery of Kenbunshoku/Observation Haki, Sanji (One Piece) is extremely alert to any and all danger around him.
Ka Rin, Heroic Woman Commander of the Land of Chu (Kingdom)