I watched my first ever episode of Doctor Who around the age of 5/6 with my mum. I insisted on getting the VHS out from the library. It was a Tom Baker series VHS and I used to get them out religiously for years (until they stopped having them there for some reason).
It's the earliest tv show I can think of that I watched that wasn't 'the norm' that wasn't princesses being rescued by princes or teddy bears flying around in a hot air balloon. It challenged me, at that very young age, to think outside the box and reconsider that we aren't the only beings in this ever expanding universe. Etc etc. I still love the show now and it is my go-to in the 'dry spell' television wise.
Movie wise there are many that I love, but the one I have seen the most out of any is the Rocky Horror Picture Show.. I first watched it at 11 and have seen it around 100 times - I know it word for word. It's amazing.