Armored Trooper VOTOMS: An intergalactic Mecha Story about a war that's raged for centuries and the reasons behind it. Starts a little slow but really picks up and has a fantastic finale. Also this is quite old as it was made in the 80's.
Macross: Frontier: Easily the most accessible of the Macross Series's, it's shiny, new, fast paced and generally fun to watch. The movies are also good but the series has a better ending.
Vandread: A funny Mecha Series about a Planet composed entirely of Men and a Planet composed entirely of Women that are constantly at war with each other and an accident that leaves 3 Men stranded aboard a ship full of Women. It's a little bit harem anime, a lot bit Mecha anime and is generally pretty fun to watch, even if the Copious CGI gets on ones nerves at times.
Space Runaway Ideon: Best consumed as a pair of movies (The Ideon: A Contact and The Ideon: Be Invoked), tells the story of a group of colonists who find an ancient alien ship and giant robot and get into conflict with a group of "lost humans" known as The Buff Clan. As the whole thing plays out like an epic tragedy this is "Space OPERA" in the truest sense of the word.
Birdy The Mighty: Decode: Only "sort of" a Space Opera as most of the story takes place on Earth, however it is about Galactic Politics coming to play on our small, insignificant planet so I sort of count it. Involves a Super Powered Space Police Woman named Birdy who accidentally kills a human boy and takes his consciousness into her body while he is "grown" a new one. Seems like the set up for a comedy but while there are lighter moments Birdy is much more an Action/Drama series with some light heartedness.
Heavy Metal L. Gaim: A Sci-Fi Mecha Series from Gundam Creator Yoshiyuki Tomino, essentially Star Wars with Mecha. Last member of a lost tribe with a mecha left to him by his father joins a rebellion to battle an Evil Empire. Well written and presented with some unique Mecha designs.
Lost Universe: It's Slayers in Space, has a ton of the same tropes and even takes place in the same Multi-verse. Only Lost Universe is a Funny Space Opera instead of a Funny High Fantasy.
Gundam: Gundam is a doozy to recommend as not all Gundam is created equal... some of it being very "un space opera-ey" and some of it being VERY Space Opera. Here's my "personal" viewing guide...
The Universal Century (watch In Order)
- Mobile Suit Gundam Movie Trilogy, a really excellent, concise overview of the original series.
- Mobile Suit Gundam: 8th MS Team, definitely NOT space opera but deals with a more "average" soldiers story during the war overviewed in the original Gundam Series (and movies). Really, really good regardless.
- Mobile Suit Zeta Gundam, watch the series, a little old but pretty powerful.
- Gundam Double Zeta, try to survive to the halfway point, it gets very good.
- Mobile Suit Gundam: Char's Counter Attack, a grand but tragic conclusion to the Federation/Zeon Conflict.
- Gundam Unicorn, good but wait until it's done, this is where it falls in the timeline.
- Mobile Suit Victory Gundam, the final bloody chapter of the Universal Century, excellent but DARK.
Alternate Universes
- New Mobile Report Gundam Wing, I'm not a big fan but some consider it a classic.
- Turn A Gundam, my personal favorite Gundam Series, light on the Space Opera elements but it's a really good story, it essentially feels like "Hayao Miyazaki presents Gundam".
- Gundam SEED, alright if you can get past the cheap looking animation, also this show is ANGSTY! Avoid "SEED: Destiny" like the plague however.
- After War Gundam X, also light on the Space Opera but a fun series none the less. It has the same character designer and mecha designer as Gundam Wing but is a much stronger series overall.
- Gundam AGE, VERY Space Opera but also kind of weak, a great premise with bad execution but it has a really epic scope.
- Gundam 00, honestly I didn't like this and most of it takes place on Earth anyway.
- G Gundam, Not really Space Opera.
Overall if you're only going to check out ONE Gundam Series, I would recommend
Turn A Gundam... even though it's not all that space opera-ish... it's just really friggin incredible.