Stephen: In terms of a catch all for Anime, my favorites would likely begin with Galaxy Express 999 TV. The movie was decent, but the time compression needed to condense Matsumoto Leiji's masterpiece down to theatrical size left a lot out. The problem is, the only way you will really be able to see GE 999 TV, without buying the Japanese DVDs/Blu Ray without subtitles, is via Crunchyroll or FUNimation's streaming site. There is a DVD release of the first 40 or so episodes, but the company that released the series had no idea what they were doing. It's a shame, as Discotek/Eastern Star had 999 TV in their sites, but had too many classic series in their stable when S'More picked it up.
The original Captain Harlock TV series, conveniently available from Discotek/Eastern Star is also fantastic. Another Matsumoto Leiji great.
Following that would be another Matsumoto Leiji master work, Queen Millennium/Shin Taketori Sennen Joo TV. The movie wasn't bad, but the series was the best. Unfortunately, outside of bootlegs, you won't be seeing this with English subtitles anytime soon. It not available outside of Japan as best I can tell.
Mazinger Z, another series released by Disotek/Eastern Star holds a special place for me, being the first super robot show I saw as a kid. This was turned into Tranzor Z in the US, but the original, to me, is vastly superior. Watching it now, the animation (from 1972) could only loosely be called "animation." The story is a little hokey, but I like the series anyway. I'd recommend Great Mazinger and UFO Robo Grendizer as well, but they aren't available subtitled either, at least not legitimately.
You also can't miss Gatchaman. ADV/Sentai Filmworks released the series on Blu Ray from the remastered Japanese sets, and it looks quite good. I don't like that they put the extras on disc from the DVD, then stretched them to widescreen, but so it goes. Thankfully the series is in proper 4:3 aspect ratio.
You've already seen Cutie Honey. It was good, but not amazing. Go Nagai at his finest, even if they toned it down from the Manga. New/Shin Cutey Honey was pretty good as well. Cutey Honey F (Flash) was a Sailor Moon kind of take on Cutey Honey. Which is funny, since CH kinda started the whole magical girl thing...
Devilman the TV series was pretty good as well. Go Nagai once again. It's pretty old, and it's available from Discotek/Eastern Star (sensing a pattern? lol). It's toned down from the Manga, and it's nowhere near the violence level of the OVA/OAV series.
Space Battleship Yamato, better known as Starblazers to we Americans (I never saw this on TV, I'm a hand full of years to young for that), is also quite fantastic. There is a decent BD release (bootleg) available of the original show with English subtitles. Glad I grabbed that. It's a lot better than the US Starblazers release because, well, it's not censored and not compressed for time. I've only ever seen the first series of the 3 in Japanese. Starblazers isn't bad, but it's getting stupid expensive on DVD.
Mobile Suit Gundam, what kicked off the more realistic robot action (instead of super robots with special powers) is pretty good too. The US release is OK (if you can find it), but it's missing episode 15. And it's either dubbed only, or subbed and dubbed, but ridiculously expensive on US DVD. There are times I recommend bootlegs... Gundam Z, and ZZ from the same era are great as well. Again... have fun tracking down either, unfortunately.
One can't look at the 80s without remembering Robotech. And more importantly, one of the series that made up that amalgamation, Super Dimensional Fortress Macross. I can't recommend Macross, the original Japanese series, enough. Robotech was OK, but I felt smooshing all those series together caused damage to all of them. Of the 3 series that made up Robotech, I think Macross stood the test of time better than the others. It's a classic.
From a comedy perspective, Urusei Yatsura is a lot of fun. It's also ridiculously long (thanks to Takahashi Rumiko, who also gave us Ranma 1/2 and Inu Yasha), so if you only pick up a few discs of it, you might get your fill. I loved it from start to finish though. And with Takahashi's work, Maison Ikkoku is also quite fantastic. Good luck finding that.
Dirty Pair TV is fun, and available on DVD in a box set. You can also get boxes of all the OVAs as well.
Kimagure Orange Road is another fantastic series. It's slice of life, and it's a complete classic. Tracking that down for a decent price will be a heck of an affair as well.
Patlabor TV, OVAs, and especially the movies (released from 1989 for the TV series, with the final movie releasing in early 200s) is a fun show, with absolutely fantastic movies. Mamoru Oshii had his hand in the first two movies (not sure on third) and it shows. For Oshii, you can't miss the original Ghost in the Shell movie, or the sequel either (both are past 1980 lol)
You can't miss Akira. You've likely seen it, but if not, FUNimation's Blu Ray release is quite good.
Ninja Scroll is an Anime classic. In America at least. And it's quite good in my opinion.
Top wo Nerae! Or, Gunbuster as it is better known in the US, is a series that will put your mouth on the floor. Well, maybe not, but it's quite a fantastic series, well worth the effort of tracking it down. There's a Japanese Blu Ray release as well, but it doesn't have subtitles, which is sad.
Nadia the TV series is quite good as well. Sentai just released a Blu Ray set for cheap that looks amazing.
If you want a contemporary movie that blew me away, check out Time of Eve on Blu Ray (think there's a DVD edition as well). It's a touch expensive, given how it was released in the US (they collected money through Kickstarter to fun the international release, so the final product being on Amazon's virtual shelves is pretty amazing). Great story, thought provoking, and well written.
There are plenty more to go, like G Gundam (Gundam take on super robots), anything Studio Ghibli, etc but I need to be done for today. Legend of Galactic Heroes is amazing too. The problem is the Japanese only release on DVD is insanely expensive, and lacks subtitles. My Japanese isn't good enough to understand it.
I think I'll do a part 2 tomorrow or within the next few days. Stay tuned and healthy.