Do you mean just from 1966-69? Let's see, that would exclude The Addams Family, The Munsters, and My Favorite Martian, which all ended a few months before TOS began, but they were no doubt on in syndicated reruns at the time. Looking over Wikipedia's category list of 1960s American TV series, and counting both SF and fantasy shows that aired contemporaneously with TOS, there's also:
Batman
Bewitched
Captain Nice
Dark Shadows
The Ghost and Mrs. Muir
The Green Hornet
I Dream of Jeannie
It's About Time
Mister Terrific
Tarzan (maybe -- I don't know how genre-heavy it was)
I'd also make a case for Gilligan's Island, which often had SF/fantasy elements, and maybe for downright surreal sitcoms such as Green Acres and The Monkees (the latter of which featured aliens in its final episode). Most of the shows listed above are sitcoms; Captain Nice and Mister Terrific were short-lived superhero comedies knocking off the Batman craze, and It's About Time was about astronauts who went back to prehistory, though midway through its lone season, it was retooled with the astronaut and caveman characters coming to the present.
There were also animated shows like Filmation's various DC-superhero cartoons, Fantastic Voyage, and Journey to the Center of the Earth, and Terrytoons' The Mighty Heroes. And then there were the spy shows that often had SF elements, like The Avengers, Get Smart, The Man from UNCLE, The Girl From UNCLE, Mission: Impossible, and especially The Wild Wild West.
Looking at the list of 1960s British TV series turns up a few more:
DoDo, The Kid from Outer Space (animated)
Haunted (short-lived supernatural series)
The Prisoner (of course)
Witch Hunt (another short-lived supernatural series)
And of course Gerry Anderson's Thunderbirds, Captain Scarlet and the Mysterons, and Joe 90.