Irene Belserion (Fairy Tail); after becoming a Dragon and being granted a human body
Kyoka (Fairy Tail)
Baldur (God of War)
The Watcher (Heroes)
Akihiro Daken (Marvel Comics); via pheromones
Cameron Cole (Red Queen)
Virgo Shaka (Saint Seiya); via Ring of Heaven's Treasure
Grayroad (The Seven Deadly Sins)
Alec (Twilight Saga)
Idol of the Three Wise Monkeys (Jackie Chan Adventures)
Rachel Pirzad (Alphas) can turn any of her senses "off" at will.
Kaname Tosen's (Bleach) Bankai, Suzumushi Tsuishiki: Enma Kōrogi creates a dome which forms a void that nullifies the senses of spiritual energy, sight, sound, and scent within its range.
The spell that made Baldur (God of War 2018) invulnerable to everything except mistletoe also had the unintended side effect of rendering him incapable of feeling anything, including taste, smell, pain and pleasure.