Since I'm the dude with the City Hunter icon, I'll give you my list which I'll break down to TV series, OVAs, then features. I'm sure you've seen a TON of these and everybody in here has made excellent mentions, so here's mine:
TV SERIES:
-City Hunter 1, 2 are by far the BEST of the TV series. Sunrise was at it's PEAK with excellent animation and color. 3 and '91 are great fun as well, but for the look, CH1 and 2 are to die for.
-Slam Dunk. In Thailand, SD was massive but I wasn't able to watch until my girlfriend (from China) really pushed me to see it. It does NOT disappoint. When me and my GF were in the 2nd year of our relationship, we would watch it back to back. Great anime which really harkens back to the days of youthful optimism (kinda why it's so popular in Asia).
-Patlabor. Underrated in that the mecha aren't really the main focus. It's hilarious and well directed. It starts a bit slow but really rewards your patience. The Chinese cuisine episode is one of THE best!
-Z Gundam. Want a soap opera with robots? This will do the trick for ya. I wanted to recommend the original but that's from the 70s. Kamile is a dick but then even bigger assholes come into the fray later on.
-Hokuto no Ken. Nuff' said. Toei's got a penchant for short changing animation sometimes, but it's history -making stuff. I remember showing the entire show to my girlfriend and she loved it! A must watch!
-Cowboy Bebop. Nuff' said.
-Much of Rumiko Takahashi's stuff is well done too. (i.e. Ranma and even, dare I say Inu Yasha. Have not seen Maison Ikkoku)
-Mospeada. We all like Macross but give Mospeada a try. Bike that turn into robot suits? FTW!
-Votoms: Slow at first but heats up when you get to Kunmen jungle wars. Part 4 becomes hella existential though and very far out!
-Captain Tylor.
OVA:
MD Geist: Big stupid violent fun from Koichi Ohata. Every single trope about American action movies you can find on this, and many other OVA.
Urban Square: Jazzy ova about a punk screenwriter who stumbles onto a counterfeiting plot. Recommended. You can read my review of it
here.
Crying Freeman: Yeah, it's a bit hard to get into (pun intended), but it's still a marvel in animation. OVAs 1,2,5 and 6 are great. 3 and 4 suffer so much which is sad since the manga arc are so intense.
Mad Bull 34: NYC cop ravages criminals. Lots of T&A here.
Wizardry: I shit you not. Go find it on YouTube. Very straightforward but fun!
Gatchaman '94: Yasuomi Umetsu's take on the Battle of the Planets TV show into 3 OVAs. Well made and summarizes the original show well. Great directing as well.
Fatal Fury: Halfway decent OVAs of our favorite SNK series. 2 is da best!!!
Devilman: Well animated horror the lord of all things, Go Nagai. Bloody good fun!
Legend of the Galactic Heroes: The greatest OVA series of all time with 108 episodes. Like tactics and space ship battles interspersed with galactic history and politics, look no further! HIGHEST RECOMMENDATION!
-Patlabor's many OVAs. Great stuff indeed.
-Cyber City OEDO. Amazing stuff by Kawajiri. Highly recommended.
-Casshan (not sins, the OVA).
-Black Magic M-66. Feels like the terminator and 80s horror film with Blade Runner esque vibes. Great action.
-JoJo's Bizarre Adventure. The original OVA from the 90s is nothing but pure excellence. Great animation with ORA ORA ORA moments galore!
FEATURE FILMS:
-Porco Rosso: Great Ghibli film. Everyone's mentioned all the other great ones, but I love this one. Mononoke and Castle of Cagliostro are also good. Girlfriend is recommending me to Castle in the Sky.
-Dagger of Kamui. THE ninja anime film for me growing up. Intense ninja action set on an epic, historical scale. It's a looong movie but well worth the price of admission. Oh yeah, he meets Mark Twain.
-Anything Kawajiri.
-Totoro. Have kids? Great way to introduce the wonder of anime to them.
-City Hunter .357 Magnum. Just a big episode featuring big sappy 80s style themes, but all in good fun. The music is amazing!
-Legend of the Galactic Heroes films. If you love the OVA, I highly recommend the movies.
-Hokuto no Ken the movie. Save your goodbyes lardass because you're already dead!
-Patlabor 1 and 2. 1 is much more straightforward while 2 is a discussion about the nature of war and occupation. Two different animals but great to watch.
-Wings of Honneamise. Great stuff from Gainax featuring music from Ryuichi Sakamoto. Very entertaining and uplifting, yet the main character somehow gets away with attempted rape.
-Vampire Hunter D and Bloodlust. The first is directed by Hokuto no Ken's Toyoo Ashida and is highly recommended. Bloodlust is obviously from Kawajiri, so it's a win win.
-SF2. As video game adaptions go, still one of the best IMHO.