Perhaps due to the kind of books I grew up with, I never had much taste for sci-fi and fantasy.
When I was quite young (like 7-9), I did read books that could be classified under those genres. 'The Dark is Rising' series by Susan Cooper, 'The Hobbit', '20,000 Leagues Under the Sea', 'Frankenstein', 'Dracula', some short story collections by Poe and Kafka. I also liked 'Dr. Doolittle', 'Treasure Island', started into the Agatha Christie when I was around 10, then ate through all the Christopher Pike books available in the then-tiny Young Adult section of the bookstore.
But for some reason when I hit my teenage years, I got sucked into contemporary. Perhaps, in that stage of growing up, I was seeking something 'real' and felt it was necessary to throw off the silly fantasies of childhood. I was still pretty childish though. A 'late bloomer' if you will, so I never latched onto anything with romance as the main plot. Agatha Christie, Poe & Kafka had left me with a taste for murder and darkness, so I read Clive Barker and some of John Saul's books. I discovered Jostein Gaarder, Haruki Murakami, Banana Yoshimoto and a whole stream of authors who only ever wrote one or two books before fading away into obscurity... but each of them often had just a hint of something strange, something not quite 'real'.
I'd have to say that I didn't read anything that was strictly 'fantasy' until a couple years ago (I know, I was way behind in the game...) when I eventually (and somewhat begrudgingly) picked up the first couple Harry Potter books. They didn't suit my taste, so I didn't get beyond the third one (I think). I figured, since the books were so widely popular, that I have given the genre a fair chance, and went back to reading contemporary and non-fiction.
In this last year, I've made a decision to spread my reading-net. Since I'm pretty ignorant about other genres, I've been asking other people for the names of authors and books that they like.
Some have been absolute misses, where I can barely force myself to get through the pages (I always finish what I start), but there have been some surprising hits as well!
I just finished reading a sci-fi book by Mike Resnick called 'The Dark Lady' and absolutely loved it. Without someone recommending it to me (thanks, L!) I never would have picked up the 'Hunger Games' books. I read a classic YA fantastical trilogy by Garth Nix (Sabriel, etc), a sci-fi YA trilogy by Patrick Ness (The Knife of Never Letting Go, etc), and even a few books with reasonably prevalent romantic-subplots. A few were enjoyable, despite the grindingly obvious conclusions, one was disappointing as I had been quite excited about the author's reputation and the premise (which was nice and dark).
I'm still leery of the whole paranormal/romance genre, but I think I'm going to dabble a little more in the sci-fi genre and perhaps try a historical fiction or two. I know Laurie Halse Anderson has one about the yellow fever epidemic... so I might start there.
...I may even try a paranormal-type book if there's a good one without the standard love-triangle plot.