Ghosts (Various Media); can be seen by people with supernatural senses
2LDK Apartments (My Room has Become a Dungeons Rest Area); to anyone from the Dungeons
Seikain Jogakkou (Shomin Sample)
Due to the fact he doesn't like adults and/or his age, Youngblood (Danny Phantom) can only be seen and heard in the presence of children and never by adults or teenagers who possess an adult mind like Jazz Fenton.
Shinigami (Death Note) can only be seen by those who have come into contact with a Death Note.
The Foretold (Doctor Who) could only be seen by the person it was about to kill.
The Krafayis (Doctor Who) was invisible to everyone but Van Gough due to his unique perception.
Mavis Vermilion (Fairy Tail) can only be seen by members of Fairy Tail guild who bear the Fairy Tail insignia.
Thestrals (Harry Potter) can only be seen by those who have witnessed someone die.
Fool (Kaleido Star) is invisible to all but those who are destined to do great things on the stage and/or those whose hearts are completely dedicated to it.
The Shinigami (Naruto) could only be seen by the user and its active victim.
While the Wendigoes (New Blood Interactive's DUSK) appear to be invisible, their ability can only be shut off once they are hurt.
SCP-870 - The Maybe There Monsters (SCP Foundation) is an anomalous species of animals that can only be seen by individuals suffering from schizophrenia.