I clicked on this thread expecting Anime that defined the genre in one way or another, this is a lot deeper than I was ready for.
To be honest I had to read my full list of watched anime and reminisce about a few things before writing this, most of my "defining" experiences are small bits that eventually turned into foundations for bigger things, I would not say any single Anime changed my life, at least not directly.
I don't remember the first Anime I watched, but the first one that made me reconsider Anime as a medium was Code Geass, it was for all intents and purposes - to me - the Anime of all Anime. It took me a while to find anything that compared to it, the scale of the story, the chemistry between characters, Lelouch's various faults being subtly displayed until it all gathers into the episode Lelouch kills his father, these were not things I had seen before, and even the first few episodes of the first season had me interested beyond the usual rate I usually were.
I eventually removed it from the "My Favorite" pedestal but it set the bar for Anime I considered 'good'.
I've watched over 300 Anime by now (hoping for 400 by the end of the year) and nothing's really taken its place since then, I tend to like a certain kind of Anime these days but even among those I cannot name a favorite. Closest perhaps would be Aria the Animation for the simple fact I watched it and enjoyed every episode, as well as to the fact it lends itself a very sweet and pleasant experience with no bad episodes. Everything in the world it portrays is "perfect", a world so beautiful and full of wonder that even Aqua itself wants you to see it.
The experience in later episodes, which is to say, the last and second to last episodes(?) complements the show very well, and it's something I thought was overused in Aria the Natural, it does not happen every single episode, but it did have times each episode would have its own supernatural twist, to the point it no longer made Aqua feel like the magical utopia the first season portrayed it as.
As for the Anime which gave me my current preference for picking out Anime to call "good", this is going to sound tiring given the rest of the posts in the thread but Clannad presented to me an emotional experience I did not expect from it, despite having known it would be a good show, and left me wanting more. Thankfully After Story exists, and unfortunately that only made me change my preferences almost completely. I won't try and sell you it as I did with Aria and (half-assedly) with Code Geass (as you've probably already watched it), not just because of the previous posts, but also because if you're posting in a Forum with obvious references to it, and whose owner is always seemingly talking about it, you might as well watch it.
Really though, anything I've watched of Maeda Jun's has received a very high score from me, and is a name you should know. Kanon, Clannad, Little Busters, Angel Beats, and many others. Even excluding those mentioned in this thread, there's a very good chance that the dedicated Anime watcher has heard or seen at least one of these or another of his works.
His stories are often very similar, from the focus on the people in your life as the story, to white-haired girls, I wouldn't say he writes the same story every time, but it's definitely noticeable. I speak of this fondly however, the optimism and good moral message within Anime involving Maeda are certainly things I need and enjoy, and he at least changes things quite a bit to make it fresh. I might have something for white-haired girls in Anime too.
I've gone out of my way to watch things Maeda Jun is or was involved in, and (You) should too.
Monogatari for its "Saving others" and "Saving yourself" schtick, which sounds somewhat ridiculous to me, but has genuinely helped me with people in my life, more than once. Psycho-Pass for its very good social commentary which I laugh at every time it (somehow) comes true. Higurashi for the best rendition of the power of friendship. Madoka Magica for teaching me to always try, even if I must defy insurmountable odds.
I could name more but they aren't as relevant to my daily life and this post's long enough as it is.
