A combination of manga and anime. It’s also 11pm at night, so forgive the low-effort post. Ordered in no particular order.

Monster by Naoki Urasawa. (manga).

A masterpiece. I read this every few years, so I can go into it completely fresh. Excellent ending, and is nearly flawless. Definitely my favorite of this mangaka’s works.

Majin Tantei Nougami Neuro by Yusei Matsui. (manga; AVOID the anime).

This mangaka went on to create Assassination Classroom. The art starts as trash, but the horror is clear in this manga while still having an upbeat tone. The main antagonist is by far one of the scariest antagonists in manga, but all the characters here are excellent. Aside from that one character. You’ll know him when you see him.

Gankutsuou. (anime).

This anime has problems with its protagonist and its female characters, but the story and drama is top-notch. Art is decent, and it’s just all very satisfying and fun.

 

Seconded Monster as the greatest manga. I don't think I need to go into why.
After that my favorite is Clannad. It was one I never expected to enjoy, and I'm sure there are ten more just like it, but it was such a good story that I had to write a fanfic about it.
The complete works of Itou Junji. The man writes short stories; it's not really fair to pick out any one of them as the best. There have been a few longer stories here and there, but where he really shines is in the anthologies of episode-length short stories that will probably never get turned into an anime after all this time.
After that there are a ton of honorable mentions; things I just can't rate any higher by virtue of not being one-of-a-kind masterpieces. Dragon Ball is a more interesting story than you initially realize; there's a video called 'the strength of Son Goku' that explains how it works really well. Fullmetal Alchemist is among the shounen greats and really both versions were good; the fact that the 2003 anime just did whatever it wanted was as much of a selling point as it was a criticism. For what it's worth, if you start watching Detective Conan now and watch it once or twice a week, it'll probably finish before you catch up.

 

Death Note probably qualifies. Amazing characters, themes and a model for good exposition.

 

Hunter X Hunter is overwhelmingly the best shonen anime I think. I can't say it's a completed Manga, but the anime does leave at a satisfying conclusion. I've only seen the Japanese sub.

I liked Serial Experiments Lain too.

 

Right off the top of my head, the top 3 anime/manga I've seen would be:

1) Yu Yu Hakusho - It's great. Immensely satisfying character arcs for pretty much every character, and the best tournament arc in any anime ever. I go back and spend a weekend binging it every few years, and it holds up pretty well.

2) Trigun - It's got some excellent storytelling and characters that are just fun to watch, even in the super serious moments. Strongly recommend.

3) Rurouni Kenshin - Kenshin himself isn't my favorite character, not even close, but the series does some really great things with plotting and character development that work great. The anime is sorta whatever, but the manga is A+ and I love it.

Honorable mentions:
-Bleach. Manga only. The anime is a whole heap of filler trash, but the manga starts of as one of the best shounen manga of all time, and starts to only slightly drop asthe series progresses. It's fantastic the whole way through. And before anyone asks, it ends after Aizen is beaten, with chapter 424, and no one can convince me their delusions of another 200 chapters of the series actually exist.

-Mx0. I dunno if this one has an anime adaptation, but this is one of my favorite manga, despite the fact that the publisher cut it short by a couple dozen chapters and there's all kinds of plot threads just left dangling. I adore what's there, and every time I'm reminded of that cliffhanger, I die a little more inside.

 

Anime-wise, I'd say my tops are: (But they change all the time)

Black Heaven (https://myanimelist.net/anime/1025/Kachou_Ouji) - A software engineer has a mid-life crisis so starts playing rock and roll to destroy an alien fleet.
Eden of the East (https://myanimelist.net/anime/5630/Higashi_no_Eden) - A death game with surprisingly good character arcs and doesn't wear out its own welcome.
Hikaru no Go (https://myanimelist.net/anime/135/Hikaru_no_Go) - A teenager is possessed by a spirit of an ancient Go player, and plays go. Surprisingly a tear-jerker ending.
Kekkai Sensen / BBB (https://myanimelist.net/anime/24439/Kekkai_Sensen) - A city (NY?) is transplanted into a monster dimension. This follows a grroup of people who .. do stuff in that city? This has *really* crazy worldbuilding and animation. I'd love to see more of it, although it's not been very popular unfortunately.
Baccano! (https://myanimelist.net/anime/2251/Baccano) - A bunch of immortals meeting up on a train.

(Edit: I forgot Steins;Gate. That probably replaces Hikaru no Go on my list.)

Not in my top, but I enjoyed:
El-Hazard (https://www.anime-planet.com/anime/el-hazard-the-magnificent-world) - pretty simple fantasy story.
Full-Metal Panic (https://www.anime-planet.com/anime/full-metal-panic) - A career soldier meets an ordinary high school girl. Played straight for comedy. It has the *weirdest* tone shifts between seasons.
Those Who Hunt Elves (https://www.anime-planet.com/anime/those-who-hunt-elves) - A bunch of people with a tank get isekai'd to another world. This is *quintessentially* anime. The tank gets possessed by a cat.

Manga-wise, I enjoyed Psyren quite a lot, although I don't remember much about it anymore. Bakuman was a great run while it existed too.

 

I'm going to be boring

Cowboy Bebop

Neon Genesis Evangelion

Baccano!

Toradora

Anohana

Runner up: Fate/Zero and Fate/UBW

 

my top 4 have already been said above (Trigun, yu yu hakusho, Kenshin, Bleach). Thank you Toonami, and then Kazaa.
so my fifth:
Avatar the Last Airbender- Its fun for the whole family, and importantly, tells a damn good study without needing to get dark.

so some honorable mentions:
Outlaw star: this was my first anime after DBZ, and I think its well described as a scruffier Bebop with more sillyness.
Gurren Lagann- I still cry like clockwork at the second to last episode, so much so that my wife laughs at me about it. it has a true roller coaster of quality, but in the second half they figure out to save all the budget for the end, and its worth it.
She-Ra and the Princessess of Power - This is an excellent character drama set against the backdrop of war, with a perspective on child soldiers, war crimes, and brainwashing that would still sneak through Nickelodean censors. And it has catgirls, but this is anime after all.

qualified mention:
Escaflowne. I love it, but i recognize it has a whole cruise liner of flaws.

 

1 Fullmetal alchemist brotherhood
The only anime that I think anyone can enjoy

2 Monster
Best of the best, but not for everyone

3 Shiki
The animation isn't great, but the manga, the story, and the music in the anime are all unforgettable to me. And don't let the start of the story fool you. For the first half you'll think you know where it's going

 

Ghost in the Shell: Stand Alone Complex.

Favourite scifi of all time.

Cowboy Bebop.

4th or 5th favourite scifi.

Madoka Magica.

Expectation breaking, several excellent twists and also really sad. I don't have any shame admitting I cried watching this.

To be contrarian, I could not stand Full Metal Alchemist.

 

Current favorites in no particular order.

Anime

Turn A Gundam: Very different from most, if not all, other Gundam shows. It's self-contained and not connected with another series, so no pre-existing knowledge about Gundam is needed to watch it.

Cross Game: Baseball anime that, like any good sports show, is driven by the characters and their relationships way more than the sport itself.

Redline: An absolutely amazing and gorgeous movie. Super Eyepatch Wolf did a better job than I ever could to explain why this movie is worth watching.

Manga

20th Century Boys: By the same creator as Monster and just as good.

Akira: A genre defining classic. The movie was made while the manga was still in progress so the two diverge a lot.

Nausica of the Valley of the Wind: Another manga with a movie that is good but also very different. Drawn and written by Hayao Miyazaki, this manga is his best work to date.

 

I don't watch a lot of Anime, but there are a few that I absolutely love.

Top 3:

My favourite of all time has to be Madoka Magica. It constantly defies expectations while telling a very compelling story. It's short, sweet and sad. But in a good way.

Hunter x Hunter is a great adventure.

Fate Zero is the best anime adaption of the Fate/Stay Night VNs, which is the only VN I ever read.

Honourable mentions:

Lelouch of the Rebellion.

Death Note.

There's possibly a few that I'm forgetting, but all of these had a definite influence on my life.

 

CHED, my buddy my pal.

I was going to come in here to say FMA:BH and that's about it lmao. There aren't many anime I don't just drop or lose interest in. That one kept me throughout - somuchso I actually bought all the brotherhood manga like some kinda weeb.

Also wholeheartedly agree re Naruto. The very first arc to Waves. When everyone was still acting like ninja and not Saiyans is still my fav. Completely lost interest post timeskip.

There are some I've watched lately that show promise, but aren't completed yet so we'll have to see.

I consider One-Punch Man finished after S1 lol, so there's that too?

Edit: I should probably add Gundam 00, given I have Setsuna's fucking gundamn sitting on my shelf and all...

 

It's more complete than the travesty of an ending that Yu Yu Hakusho got. The author is famous by now for abandoning stuff; the anime finished in great location and could easily be considered complete. The manga on the other hand is like 17 chapters into a new arc...

 

Code Geass was pretty neat. Naruto, I suppose. Bleach as well.

I also adore sport animes, even if they're often formulaic af. Kuroko no Basket is one of my favorites of that genre. Major is also a good finished series, even if the seasons differ in quality.

Fate is good, too. At least most of the Ufotable stuff and Fate/Zero.

Too lazy to make a Top 5 out of it, but those are some of my favorites.

 

Holyland and Tower of God are my definitive top two. Third is a little bit harder to peg. Kingdom, Beelzebub, Solo Leveling and Shokugeki no Soma (before its late series turn into a rotten pumpkin) are all in contention.