King of Braves GaoGaiGar
On a winter night, a mysterious mechanical lion came flying in front of a married couple, carrying a mysterious baby with it. As they took the baby in, the lion left them in confusion. About 7 years later, the space shuttle Spirits, in which high school astronaut Guy Shishioh is a passenger, collides with an unknown object bound to Earth. Despite being mortally wounded, he is rescued by the same mysterious lion and returns to Earth. In his hand, he holds a mysterious green jewel as Leo Shishioh uses it to revive Gai into a cyborg.

Two years later in 2005, the mysterious baby under the care of the Amami couple, now named Mamoru, is living his life normally. This until the mysterious group known as Zonders begin their invasion of Earth. As a response, the Earth Defense Brigade Gutsy Geoid Guard, or GGG, was organized to fight against the Zonders. In an attack by the Zonders, the mysterious boy encountered Guy, who is now a member of GGG. Equipped with the green jewel, known as G-Stone, he becomes the pilot of the lion robot that saved him. Named Galeon, he fuses with it alongside 3 assist vehicles created by GGG to become the giant robot GaoGaiGar. After the battle against one of the Zonders, GGG discovered that Mamoru can purify people who became Zonders and wondered about his origins and how it was linked to the appearance of the Zonders.

--A STRONG contender for my favorite anime period, Gaogaigar is the final entry of what's known as the Brave Saga, a collection of series aired between 1990 and 1998 based on toys made by Takara, who also made Transformers. Each series is unconnected except that each one is about Brave Heroes (and sentient giant robots. Lions are often featured in some way also.) Sharing a universe with Betterman, (which is another show I'd forgotten about, see below), Gaogaigar has proven to be much more popular than the others, with a sequel OAV series (GaoGaiGar FINAL, which also had a TV re-edit Grand Glorious Gathering) and a manga light novel and sequel King of Kings: Gaogaigar vs Betterman, along with being a perennial favorite in Super Robot Wars ever since @lpha 2. If you like hot blooded yelling, the power of COURAGE, and the letter G Gaogaigar is the way to go. And Discotek is bringing the entire series to America (finally) in winter 2023! In the meantime, a long, long out of print dub exists of the first 25 episodes, with the rest of the series subbed, by Media Blasters, apparently. If you can acquire copies before then though, please give it a watch! Then buy the blurays, because it's worth it.

Betterman
The year is 2006, a series of seemingly random terrorist attacks rock the globe. Dubbed "Algernon", normal people suffer psychotic breaks and begin murdering everyone around them - often in profoundly disturbing fashion. In the wake of traditional law enforcement's failure to turn up any link between these incidents, a private contractor known as Akamatsu Industries is brought in to explore if Algernon is a disease, an unknown terrorist group, or even more exotic possibilities.

Meanwhile, a mysterious mass fatal accident occurred while preparing for the opening ceremony at the geofront type underground amusement park "Bottom the World". Asami Toko of the Algernon research institute "Modi Warp" who visited the investigation with the authorities, concluding that the accident was caused by Algernon. Around the same time, high school student Keita Aono accidentally stumbles inside the prototype Neuronoid Kakuseijin 01 in which is piloted by a girl named Hinoki Sai, his childhood friend he hasn't seen in years, and on board the cockpit as a rare "Dual Kind" head diver. In their exploration in the "Bottom the World" in hopes for them to escape, they both find out the mystery behind the Algernon phenomenon and the mysteries surrounding the mysterious man named Lamia who is classified as a "Betterman".

--This one is much closer to horror, or perhaps psychological thriller-horror, than anything else. It's been a long time since I watched it, and I wasn't super into it at the time, but not because of quality issues, it just wasn't super my bag back when I watched it...probably around the early 2000s. Apparently this was the first anime aired in widescreen (Though letterboxed).

Record of Lodoss War
Record of Lodoss War recounts the adventures of a youth by the name of Parn, the son of a dishonored knight. Part of his motivation for adventuring is to find out what happened to his father, and to restore his family's honor. Despite his inexperience, Parn is considered the leader, who is accompanied by his childhood best friend Etoh, his friend and sometimes advisor Slayn (and later by Slayn's lover Leylia), and his newfound mentor Ghim. They are accompanied by Parn's romantic interest, the high elf Deedlit, who comes from the Forest of No Return seeking an answer to her people's isolationism and an end to what she sees as a slow march to extinction; and a thief named Woodchuck. Throughout the series, Parn comes into contact with friends and foes alike. His allies include King Kashue, King Fahn, Shiris, and Orson; his enemies include Emperor Beld, Ashram, and the evil necromancer Wagnard.

--A classic, there's not a lot I can say about it, as it's been...25 years or so since I've seen it, and I don't remember if I saw all of it even then.

Bubblegum Crisis(This is the closest it has to an 'opening theme'.)
The series begins in late 2032, seven years after the Second Great Kanto earthquake has split Tokyo geographically and culturally in two and it also forced the United States of America to annexed Japan in the legitimate name of keeping the peace and from it descending into anarchy . During the first episode, disparities in wealth are shown to be more pronounced than in previous periods in post-war Japan. The main adversary is Genom, a megacorporation with immense power and global influence. Its main product are boomers—artificial cybernetic life forms that are usually in the form of humans, with most of their bodies being machine; also known as "cyberoids". While Boomers are intended to serve mankind, they become deadly instruments in the hands of ruthless individuals. The AD Police (Advanced Police) are tasked to deal with Boomer-related crimes.

--I shouldn't need to say much about this one here, but still, here it is. The ORIGINAL one, not BGC 2040, which I feel is a bad knockoff at best and completely nonsensical at worst. I will include Bubblegum Crash, however, which I actually did enjoy. For those who don't know, this is an 8 episode OAV series (11 when you include the 3 episode 'Bubblegum Crash' sequel)

Iria: Zeiram: The Animation
The story begins with Iria as an apprentice to her older brother, Gren, a veteran bounty hunter, and his partner Bob, who work for Ghomvak Security along with a somewhat loutish hunter named Fujikuro. During a rescue mission to a hijacked spaceship called the Karma, they discover that the hijacker is actually a seemingly indestructible alien called Zeiram that broke out of the cargo hold during transit and began to massacre the crew. Bob is critically wounded by Zeiram while evacuating the survivors, and Gren is lost while attempting to kill Zeiram by destroying the Karma. Returning to Myce, Iria finds herself targeted by assassins working for Tedan Tippedai, the corporation that owned the Karma, and discovers a covered-up plot to control Zeiram in order to use it as a weapon. Iria escapes with the help of Fujikuro and reunites with Bob, who never recovered from his injuries but had his mind downloaded into a computer program. Together they continue to investigate rumours that Zeiram has appeared on Myce, and try to find out what happened to Gren, who also seems to have survived the Karma's destruction....

--A prequel anime to the live action Tokusatsu Zeiram movies, I love this show for it's unique stylings and the strange organic mushroomy-feudal-japany technology.

Excel Saga
Believing the World to be corrupt, the secret organization Across plans to conquer the world. The first step in the plan for world domination is to begin by focusing on one city in order to minimize setbacks. Across consists of the leader of the organization, Il Palazzo, and his young adult officers: the enthusiastic and energetically devoted Excel and the soft-spoken Hyatt, who is prone to fainting and losing lots of blood at a time. Excel and Hyatt live in an apartment building in the city, along with their pet dog Menchi, who they have deemed their emergency food supply. Excel and Hyatt are later joined by a snobbish but equally clueless rival officer of Across named Elgala.

--Ah, Excel Saga. Chaos. The anime takes a slightly different turn from the manga, in that it's the anime staff forcing the original author to approve different genre shifts or gimmicks every episode.

Hinamatsuri
Yoshifumi Nitta, a mid-level Yakuza of the Ashikawa-gumi, finds his normal life thrown into chaos when a girl from the future literally drops on his head without warning. Knowing nothing more than her name, Hina, and the fact that she has incredible psychokinetic powers, Yoshifumi reluctantly becomes her de facto father. However, Hina's arrival sets off a chain reaction of events that affects everyone in the city, especially after more girls from the future arrive to bring her back or terminate her.

--Hinamatsuri is more chaos. It's really hard to describe these comedic shows, but I really do find the ones I'm recommending funny.

That's all I can think of for now. If I can think of more, or I get reminded of them, I'll either edit this main post or reply with another batch. (EDIT to replace an incorrect video)