There are fewer entries outside the UC canon, and I've seen most of them. Like many anime fans my age, my first Gundam was Wing, back when it ran on Toonami in the early 2000s. I got sucked into y fandom and mailing lists (back on ye olde YahooGroups) and even wrote fanfic. (No, I'm not telling; it may be on the internet somewhere, but I have no idea.) I haven't watched Wing since it aired on TV 20ish years ago, and I'm nervous about doing that, but I'll get around to it someday, now that I'm old and crotchety.
Some of the non-UC series are divisive among a particular type of US fan. Wing, for example, is the one with the pretty boys that caters to girls. When Orphans was airing, I had to block a dude on tumblr who kept commenting that it sucked on my posts.
Many of these series are available through streaming sites, some on multiple sites as of June 2021. The ones I know of, I'll include. Which one to start with depends on the type of story you like, so I'm listing them in order of how much I like them.
My favorite: Iron-blooded Orphans
This is a 50-episode series that ran in 2 seasons from 2015 to 2017. (There was a gap between them.) Of all the non-UC series, this is the most original-Gundam-like, and its tone is very similar to 08th MS Team. Most Gundam shows involve child soldiers (because the target audience is teenagers), and they're portrayed as normal. This one shows how fucked up that is.
Our protagonists are teenagers who are indentured to a military contractor, CGS, on Mars. As part of their indenture, they are implanted with cyborg hookups on their spines which connect to their robots and allow them to pilot better. The procedure is painful and frequently deadly. The oldest and leader is Orga Itsuka, who is all of 19 at the start. CGS is contracted to escort a rich Martian girl to Earth, but shortly after she arrives, they're attacked by Gjallarhorn. The adults of CGS send out the kids and use them as decoys while they run away. When Orga finds out and gets back to base, he and his cadre of older kids take over the company. They rename it "Tekkadan," the iron flower group.
Orga's mission is to give his family a peaceful future, which they have to fight for, because society literally considers them garbage. Some characters are referred to in the series as "human debris." Orga's quest leads him to make deals with the devil because he sees it as expeditious. He runs into a space yakuza group and joins them. There are strong anti-capitalist themes. There is mention of child abuse and child sexual abuse. It gets extremely dark (for a Gundam show, for sure) more than once, and there's a high protagonist body count.
I highly recommend this show. It's a real 21st-century one. The story and script are by Okada Mari, and it was directed by Nagai Tatsuyuki.
Where to watch: hulu, Netflix, crunchyroll, funimation.com; Amazon Prime (for an extra fee); Blu-Ray
Also good: 00
Gundam 00 is a 50-episode series that originally aired from 2007-09. It's set about 300 years from now, in the real-world timeline. The protagonists are four Gundam pilots in a group called Celestial Being, whose purpose is to stop conflict as it happens. They're kind of terrorists, you could say. But they're very powerful, so the other factions on Earth unite to oppose them. There's a magic supercomputer that calculates where conflicts will crop up, so CB can be on site to intervene. Then some super-powered people called Innovators (the Newtype analogue) show up.
Season 1 is better than Season 2, and the movie is ... absurd. (Sentient crystals from Jupiter.)
Where to watch: hulu, crunchyroll; Blu-Ray
G Gundam (1994-95; 49 episodes)
Every four years, there is a Gundam fight tournament to determine who is president of the world for the next four years. One group wants to rig the tournament so they win, and they have an overpowered super gundam, which is Devil Gundam in Japanese, but Dark Gundam in the US dub. The mobile suits are piloted in a unique way: the pilots wear clothes that sense their motion and translate it into robot motion. So the robots do the martial arts that the pilots do, which makes for interesting fight scenes.
There are a lot of Problematic(tm) things, like the national stereotype Gundams. Tequila Gundam wears a sombrero. There's a windmill for the Netherlands. These are mostly not main characters, but they still exist.
Chibodee Crockett, from Neo-America, uses his shield as a surfboard and has boxing gloves. Nobel Gundam from Sweden is Sailor Moon. The French Gundam has roses. It's absurd, which is part of its charm.
Where to watch: crunchyroll; Blu-Ray
Gundam Wing (1995-96, 49 episodes)
Five pilots from the colonies at the Lagrange points are sent to Earth to destroy the Earth Alliance, which oppresses the space colonies. They don't know about each other, but the old scientists who sent them and gave them Gundams know each other. They form a little sentai squadron and go around being terrorists. The Earth Alliance has mecha, too, and they fight each other. But there's a side faction on Earth that wants to take over for its own reasons, and things get complicated.
Where to watch: hulu, crunchyroll; Blu-Ray/DVD
Gundam Seed (2002-03, 50 episodes)
There are genetically-modified superhumans called Coordinators, who escaped to space colonies to avoid hate crimes from the Naturals. There are a few factions on Earth, including one Naturals-supremacist group. War breaks out between Earth and space. One space colony is neutral, and they get pulled into the war when space forces attack.
To be honest, I haven't watched this since it came out, but I liked it at the time.
Where to watch: hulu, crunchyroll, funimation.com; Blu-Ray
They're ok, I guess
Gundam Seed Destiny (2004-05, 50 episodes)
This picks up where Seed left off, but it focuses on a new character. The new character is fine, but the heroes from Seed are brought back as overpowered gods, basically, after fans wanted them back. *yawn* It's not terrible. Parts of it are actually rather good. But it goes downhill about halfway through.
Where to watch: crunchyroll; Blu-Ray
Gundam AGE (2011-12, 49 episodes)
I watched this when it came out and don't remember much about it, beyond that it existed. The 3 seasons of this are each from the perspective of a member of a different generation of the same family, which is kind of neat. Unfortunately, the execution was kind of a mess. The best part is season 2, because the protagonist is the coolest. Or maybe it was parts of season 3 because of the pirates? Like I said, I don't remember this very much, and wikipedia has you covered.
Where to watch: not available streaming in the US; Blu-Ray
Do not watch: Reconguista in G (2014-15, 26 episodes)
This show is just bad. I watched all of it, and I can't tell you what happened, even with the wikipedia article open. The biggest problem is that there was way too much going on in way too little space. If it had had 50 or 52 episodes, it would probably have been fine, but it's difficult to keep up with all the factions and characters and backstabbing and side changing when there's an entirely different plot every other episode.
On the plus side, the mecha and character designs are pretty cool. The mecha and character designers from Overman King Gainer were involved.
Where to watch (if you must): crunchyroll; Blu-Ray
I haven't seen Gundam X or Turn A, so I can't comment on those, and neither appears to be available for streaming in the US.
There's a meta series which starts with Build Fighters that takes place in an alternate-here, where a magical space particle lets people imbue their gundam models with magic energy that lets them fight while the model builder pilots it. It's Angelic Layer but with gundam models, and its entire purpose is to sell model kits. Even more so than the usual gundam series.
That said, it's a lot of fun. The protags are middle schoolers who enter a tournament. There are powerful groups that have dedicated money to improving their build quality (Gundam Academy) and all the stuff you'd expect from a tournament show. The characters are archetypes, but they've got a bit more depth than just "the protag" or "the rival" or "the nerd." It's fun, and it lets Gundam nerds geek out (both on and off screen) about the various kits used. There's even a bit of kitbashing!
This isn't a good place to start if you want to understand all the in-jokes. If you don't mind not getting the references, or you just really like tournament shows, fire it up!
Where to watch: crunchyroll