It's really difficult for me to choose a favorite anything because there is so much media I've consumed and I really like a lot of things for very different reasons. It's hard to say I like one more than another when they're trying to accomplish completely different things. Instead, I'll mention a few animes that especially stick out in my mind for unique reasons.
Paranoia Agent is probably the first anime that comes to mind when I'm asked this question - not necessarily because it is my favorite anime (it's definitely up there though) but because I find it to be such high quality and rarely find anyone mention it at all, no less seen it. It was created by Satoshi Kon (an anime legend, RIP) and animated by Madhouse - how I would describe it is a psychological thriller about Tokyo experiencing mass hysteria over a boy known as "Shonen Bat" (Lil Slugger in the U.S. version) who rides on roller skates and attacks random people with a golden baseball bat. Incidentally, his victims always happen to be involved in some overwhelming, psychological circumstances and each episode covers either a victim or another person related to a victim. There's also a lot of questions of whether or not Shonen Bat is real and what the attacks mean.
On the other end of the spectrum of significant anime to me is the entire Dragon Ball series. I say it's on the other side of the spectrum because, personally, I don't find it as qualitatively well done as a lot of other series I've seen. Regardless, I can't deny the impact the series has had on my life (my earliest drawings I can remember were DBZ characters, so it may have been the reason I got into art in the first place) and I still highly enjoy watching it. Even when it's "bad," there's a certain charm to Dragon Ball's "badness" that feels unique to Akira Toriyama's sensibilities and I still find myself having fun with it. I've found that I have a greater appreciation for Dragon Ball when I treat it as a comedy more than an action series, which is what Toriyama originally intended the manga to be and why I feel like Dragon Ball Z Abridged has found so much success - because the characters and world lend themselves so well to comedy.
And a third mention to round things out: Hunter x Hunter. What makes this series unique to me is how each arc seems to slot itself into a completely different section of my "enjoyment spectrum." There are a couple arcs that fit into my enjoyment of "standard shonen action done well," the Phantom Troupe arc which I would define as "exceeds shonen action standards," and the Chimera Ant arc (though it seems to be rather divisive among fans) which I find to excel as a story beyond just how it relates to other anime. A lot of anime has the "issue" of arcs being inconsistent quality-wise, but HxH has an inconsistency to its arcs in that they can vary widely on tone, storytelling technique, and focus - which I can understand might be alienating to some audiences but I am all for it.
