It is really hard to pick favourites from over 10 years of network history. I have seen so many great questions and answers from other people and also myself written so many posts I'm very proud of over the years, that this question seems almost impossible to answer, especially since all those posts are extremely different and uncomparable. However, I'll try to pick something broader pertaining to things about the SE network and specifically my usual home site of Movies & TV that make it stand out on the internet.
As to my own contributions, I would generally list my answers about Interstellar, not necessarily because these answers are so great or the best I've written (though, some of them I am indeed proud of above average, but maybe not all of them), but because the period when most of these questions were asked and answered for me marked not only the most productive period since the earliest days of the site but also the pinnacle of what the site's manifesto is talking about when it speaks of "...contributing to the appreciation of the film...".
Now the film sure impressed me a lot and that is certainly a subjective thing. But what really kept me engaged to it for weeks was that very site and its questions that furthered my delving deeper into some aspects of the film and related materials, driving me to answer some of the questions arising about it. And a lot of the questions were indeed really great too, it's not just that I like my answers to them. I even spent a good portion of a sunday evening trying to write my single only Physics answer.
And that is what the site is able to do, furthering the discussion of the things that move us, be that by posing engaging questions or writing interesting answers. It provides a platform to not only find and enjoy interesting information but also delight in writing about the stuff you care about yourself. And that all while hopefully "making the internet a better place" by filling it with useful information. (Also notice how I said "discussion", a word sometimes eschewed on SE when taken too literal. But it is this formalized and well-structured way of discussing things that the Q&A format enables so well.)
As to the contributions of others, the above mentioned problems with comparing and pinning down an exact best over all those years make this really difficult. So forgive me when again using another post of mine to point to another amazing aspect of the SE format. I am very partial to sanpaco's answer to a question of mine about a rather underrated film (Peter Weir's The Way Back, to be precise). You'll notice the question is about 4.5 years older than the answer. But not only was it a late answer, I had actually almost given up on the question. I already half answered it in the question and it also at some point got auto-deleted for inactivity.
But not only does it receive an answer almost 5 years later, it even gets an answer that provides entirely new insights I hadn't ever considered when having seen the movie a few times again since asking the question. It again absolutely "contributed to my appreciation of the film", but even more so it also showed that a question on SE is never really dead. Now fortunately our site's topic tends to be one where we can usually afford some patience for a good answer and as long as we have that, any time someone else might come around who does not only share your interest but who has the answer you've been waiting for for years.