It is always interesting to hear this same question posted on that Cinephiliacs podcast, and most of the guest's first film turns out to be a Disney one! I'm no different in that regard although I don't really remember the films themselves more than the circumstances around them. I remember my dad taking me to see The Black Cauldron (the darkest Disney film, where they even *spoiler*
kill off the wisecracking comic relief animal pal!
) and The Fox and The Hound. And I vividly recall my mum taking me to see Disney's Peter Pan when I must have been 5 or 6, though I don't exactly remember the film itself but standing in a mid-Summer afternoon queue of dozens of people going to the other films playing at the same time - A Nightmare On Elm Street and The Goonies! I particularly remember the poster for The Goonies - the one where the entire young cast are improbably hanging off of a stalagtite
- making an enormous impression on me at the time as the height of adventure! Although even at that young age I remember wondering just exactly how the heck they'd gotten themselves into that situation in the first place!
Similarly as a very young kid my parents kept certain films off limits (I still remember the 'forbidden fruits' of rented tapes of Cocoon and the Ringo Starr film Caveman placed high up on the dresser, away from prying young fingers!), but I still ended up seeing great, but still quite strong, stuff like The Goonies and The Black Hole (the other
darkest Disney film of the period!) Plus it was also the era of The Dark Crystal, The Neverending Story and Labyrinth. Lots of dark fantasy stuff to traumatise the kids with!
I don't think that I have ever picked up The Black Cauldron or
The Black Hole on DVD or Blu-ray, but they are probably the Disney films I feel stronger about than many!
But I wasn't really too much into films until my teens. There were significant moments though - I'll always treasure the memory of my dad triumphantly bringing home the much-in-demand rental tape of Who Framed Roger Rabbit? Or birthday rentals of Gremlins 2 on my 11h birthday and Terminator 2 on my 12th! (My parents were always aware of age ratings but did not mind breaking the rules occasionally! I remember a key Christmas present being given the Aliens trilogy, at that point, on VHS when I was 14 or so! The first film in widescreen too, which was a big deal for the mid-90s! I remember watching the film as much to enjoy the black bars framing the action interestingly as for the film itself at times! Little did my parents know that I had previously furtively watched a friend's borrowed copy of Aliens and Predator during some school holidays in the middle of the day, to minimise the scary factor!).
Or sleepily half-watching the Moviedrome screening of Solaris, which is perhaps the best way to be introduced to that film (falling asleep to the beautiful landscapes and Russian language, getting woken up a little by the noisy City of the Future sequence, before later on waking to see the characters on some sort of space station!). The other half-asleep film series I remember from my childhood is when a series of Godzilla films screened in late night Friday double bills. I barely remembered the contents of them, but the various 'conversational' growls and roars going on between Godzilla and the other monsters were perhaps too weird to inflict on a semi-conscious brain! I may have been left with the impression that the roar sound effects were how everybody in Japan spoke for a couple of years afterwards!
I don't think my parents shaped my tastes too much after that (though I remember the Whoopi Goldberg film Jumpin' Jack Flash was a big family favourite! And we all sat down to watch the TV premiere of (TV censored) RoboCop!) but they gave me the space and provided the resources to build on, which was the best way to be encouraged to go off exploring into horror, subtitles and then just general arthouse films, I think!
As to MichaelB's comment earlier, I remember seeing a TV broadcast of 2001 at around age 13 and that worked quite well as a touchstone film at that age! I guess the strangely complimentary 2001 and The Black Hole aren't bad, if bleak, films to anchor a childhood around!