Dropped this into the wrong section, just a slight slip-up, heh.
Tough for me to be like "THESE ARE THE DEFINITIVE FAVORITES", but this is generally anime that had a big impact for me personally.
Dragon Ball Z - Long running anime series have a problem with dragging on for way too damn long and this is a notorious series for that (Though pales compared to something like One Piece, but we all know about Frieza's "5 Minutes" on Namek), but this was the first series that really introduced me to this style of anime, of the big action, crazy moments, that anime is pretty well known for.
Princess Mononoke - This is probably one of the earlier animes I saw, stuff like My Neighbor Totoro, Kiki's Delivery Service, and likely some others. The animation is incredible and the story is pretty intense even as a young teen.
BECK: Mongolian Chop Squad - There aren't a lot of really great anime that I feel deal with music. There's a bunch that have them, especially in what feels like the past decade or less, but this handled it from a much more real perspective for the most part and had good music to boot.
Cowboy Bebop - No surprise with this, it's one of those animes that usually shows up on top lists. From the characters, to the voice acting (English Dub), to the music, to the setting, it's such a completely awesome and well rounded package.
Hellsing: Ultimate - I remember liking the original anime, not knowing about how it shifted things story wise in its own direction, so when Ultimate came out and was just like "Let's go fucking nuts", I went right along with it. It's stylish, gory as all hell without just being purely grotesque, and it's a killer action show. It's leaps and bounds better than the original anime in every area to me.
Ghost in the Shell/Stand Alone Complex - Hard for me to pick just one thing, so I'm sorta just lumping the original movie and tv show together. The first GITS has such fantastic animation with some great action, where as the show lacks some of that due to its tv show quality, but makes up for it with interesting scenarios and better exploration of all the characters. I've never been a fan of the deep philosophical elements, it goes way over my head, but GITS can be a great time. The other movies and OVA series never quite hit the same mark for me, but it's nothing super bad.
Tengen Toppa Gurren Lagann - I feel like this show is what took anime to a new level for me. Like there was always absurd nonsense in Dragon Ball or some other anime shows, but the style here with crazy animation and insane levels the series went to, especially in the second half, makes this show incredible. It's ridiculous fun and it really set the bar for what Trigger would continue on afterwards to various degrees of success.
Attack on Titan - While still a series in progress, I feel like it hits everything I enjoy with anime. A crazy setting that isn't possible in most any other medium outside of maybe gaming, the creatures are weird, but unique in execution, and the action gets awesome. It has some ups and downs and with the third season, it shows that they can better handle a downturn in pace when Titans aren't around. Like this show could end terribly for all I know, as the manga is still going, but I feel like it's a good ride so far either way.
Spirited Away - The level of quality is well known with Studio Ghibli, but I think if I was ever to show someone an anime, it would be something like this as it has a lot of that whimsy and spectacle anime is known for, and especially with Ghibli itself from earlier anime, but also has more of a slightly dark undercurrent that could be seen as a little tense for the younger watches that I remember having as a kid like with Secret of Nimh or Little Nemo.
Drawing a blank on my last one for the moment, as I'm not sure what would be right. I kinda want to put in Made in Abyss for how intense and dark it is while also being beautifully animated, or maybe K-On! for appealing to a much more chill and bubbly side of anime, while also tapping into my love of music like with Beck. Fullmetal Alchemist: Brotherhood is another possibility too.
