I have always loved to read. My favorites have always been Fantasy and Science Fiction, with a little Horror thrown in. I've had a tendency to skip some of the mainstays in favor of the more obscure.
The wonderful thing about books is that for every seemingly fresh or original idea seen in TV or movies, a book has often explored a deeper variation decades ago. The concepts are simply much more inventive in novels than you can ever conceptualize on the screen, though I do enjoy both.
I've enjoyed novels of High Fantasy, but sometimes get tired of the old cliches or writing styles of 'classic' authors such as J.R.R. Tolkien. I usually prefer fantasy stories with a strange twist or more exotic environment, or with a more pragmatic take on events.
However I also greatly enjoy humorous fantasy that has fun playing with fantasy conventions. Terry Pratchett's Disc World is one of the best series I've ever read, and each book manages a clever and amusing take on a different topic.
Sometimes it can be hard to tell the difference between alternate history, time travel, and other-dimensional stories but I would consider alternate history to be set entirely in its own divergent world. I greatly enjoy these, from extreme variations about divergent evolution to the more conventional stories of divergent historical events.
Some stories take place on an Earth with different rules, though I would only consider magic and monsters to be alternate if they are an established part of their world.
There are many versions of time travel. Some are trips into wildly speculative versions of historical events or result in bizarre timelines. Other stories play with multiple versions of a character or offer a different take on historical figures. Some of my favorites involve cabals that manipulate and profit from access to alternate worlds.
Some stories maintain a connection between strange other-worlds and our own, creating an interesting contrast. Whether through dimensional portals or magic, a modern character goes on a journey through strange new worlds. Sometimes the story is about the conflict between a character's dual heritage.
Then there is the odd category of stories that take place in some form of the Afterlife. Sometimes this is a new take on Biblical stories, or different versions of the conflict between Heaven and Hell, Good and Evil. Other times they just explore how a particular character or historical figure would react to a continuing existence after death.
Modern Fantasy would probably cover any type of story involving magical elements in the modern world and would bleed a little into the Horror category. There are stories about angels and demons playing with the fates of mortals, mythic deities in modern times, Urban Fantasy about Faeries and magic in modern cities, and probably any stories about Vampires, Werewolves, etc., that involve social maneuvering rather than a violent encounter.
Horror stories often have magic and supernatural elements in common with Modern Fantasy, but of course explore them in a more grim and frightening way. Characters either try to resist or fully indulge in all manner of dark, twisted impulses, seek macabre vengeance, or have encounters with horrifying and unnatural things. Monsters lurk about stalking human prey.
I would pretty much lump in any stories from the slightly exaggerated near-future to hard science fiction, though there are large sub-groups that I would consider separately.
There are stories of technological and genetic advances, mad scientists, and unforeseen consequences. There are alien encounters, from infiltration to mass invasion. There's Cyberpunk, about our relation to rapidly increasing computer technology and Artificial Intelligence.
I have always enjoyed the many twisted variations of this genre. From survivors adjusting to the aftermath of a disaster, to the brutal new societies struggling to rebuild. Then there are the stories of the bizarre societies that developed generations later, with their own strange traditions and alien ecology. Some of these are so exotic they veer back into Fantasy stories.
I would consider these stories to be Sci Fi that goes beyond a futuristic Earth, to space travel and off-world colonies. There are many stories of future warfare against alien threats, as well as intergalactic adventures amongst alien planets. Some are epic quests, while others are just about interesting characters and con men operating on a vaster canvas.