DrFidelius
The Shy Stegosaurus of Cricket Creek. I don’t remember the author.
I think it was Godzilla movies.
My maternal grandfather was heavily into SF (NOT sci-fi, as he would tell you)(and as I will also tell you) and I started reading SF/fantasy when I was about 8. My grandfather would occasionally give me suggestions, and I was pretty much allowed to freely browse his considerable collection. I wasn’t allowed to browse his Playboy stash (nobody knew about it til after he died) but I could borrow many of his books and read them. He was a pompous old bastard, but he did give me this hobby, so he wasn’t all bad.
Of course, by the time I was 10 or so, I was spending my own money on paperback SF novels and collections, and checking stuff out of the local library, so I was able to read fantasy (which Grandpa disliked, for the most part). My parents disapproved of just about all SF/fantasy, but they allowed me to read it, for the most part. I remember that I was occasionally grounded from reading SF/fantasy as a punishment. Of course, this only made that genre even more attractive…
Edgar Rice Burroughs took me for the first time into the pleasures of off-planet fantasy. A virginal copy of Tanar Of Pellucidar and I shared the journey and were both quite spent after multiple rereads. Burroughs has a fair body of thoroughly readable work.
hmm…I don’t recall a defining moment, but it probably had something to do with seeing Star Wars when it came out in theaters and watching Creature Double Feature on Saturdays.
God, I loved that book as a kid! Here’s the info, from Bibliofind:
Evelyn Sibley Lampman: The Shy Stegosaurus of Cricket Creek
Totally freaked out a grade-school teacher who assigned a “what pet do you want?” paper. I wanted a dinosaur.
Veb
My mother. I remember watching Outer Limits, Night Gallery, Star Trek, Dark Shadows and the Twilight Zone with my mom before I was old enough to be watching that stuff and which probably accounts for my rather vivid imagination. 
I think the first Sci-fi I read was Stranger in a Strange Land and Have Spacesuit, will Travel in 5th or 6th grade. It’s been so long, I can’t be sure, but that’s one of my earliest recollections.
Star Surgeon by Alan E. Nourse, read that in 1961 at age 9.
was hooked on sci-fi since then. was watching the start of the space race on TV and reading about colonies in the asteroid belt revolting against earth. the nuns didn’t teach squat about science. i was building model rockets by 7th grade. who needs nuns.
was able to order a copy of Star Surgeon from amazon.com. took them weeks to find and cost $60.
Dal Timgar
Bawdysurfer wrote:
So, did the Earth move for you, too? 
Erin Gray.
My father had a bookcase full of paperback SF short story collections from the forties and fifties. Things like “The Year’s Best SF from Astounding Science Fiction, 1952”. I grew up on these, and they gave me a permanent preference for short stories vs. novels.
In the sixth grade I had a fantastic teacher(his first year) who liked science fiction and fantasy. It was also the first year of the original Star Trek. Mr. Bradbury had us write sci-fi stories for practice. He read us a chapter of The Hobbit each day. All these things together got me “into it”.
Well, apart from watching Star Trek, I’d say it was Madeleine L’Engle’s A Wrinkle in Time, when I was in 5th grade, then sneaking a read of Haldeman’s The Forever War when I was a few years older than that. I was hooked forever.
I can’t remember not being interested in science fiction. My older brother was into it, so I got lots of exposure to it.
We had a vinyl 45 with a “Tom Corbett, Space Cadet” story on it (“From the rocket fields of the Academy/to the far flung stars of outer space/We’re space cadets training to be/ready for dangers we may face!”)
Don’t know if this qualifies, but we also had a 78 of the popular kids record “By Rocket to the Moon.” Kind of SF/educational. It contains a ditty that I learned the names of the planets from (superseded by Schoolhouse Rock’s Interplanet Janet, I believe).
My brother recorded a reel-to-reel tape which contained two episodes of the radio show “X Minus One.” The episodes were “Early Model” and “Man’s Best Friend.” I played that tape hundreds of times when I was a kid. I recently listened to MP3s of those two episodes, and when I would hear a line, about 2/3 of the time I could say the next line exactly, including the actor’s interpretation.
I have definite memories of “Science Fiction Theater.” Also, in the early 60s WGN broadcast the “Flash Gordon” serial on Sunday mornings. “Twilight Zone” came a little later.
Books - I also read “Spaceship Under the Apple Tree” at some point, also from a bookmobile (in Chicago). A bit later I read the “Tom Corbett” books, and still later borrowing my brother’s copies of Asimov, Heinlein, Clarke, and others. Asimov is still my favorite.
Miscellaneous: the Classics Illustrated comics of “War of the Worlds” and “The Time Machine” and some sporadic SF comics. Don’t know if Superman comics et al. would qualify. Also one or two Tom Corbett ViewMaster adventures.
I’m embarrassed to say it, but for me it was Andre Norton’s “Galactic Derelict”. I was in 5th grade, and I went on to read all of her books before I ever discovered there were other SF authors, who wrote much better than she did!