My first true exposure to anime space opera was Legend of Galactic Heroes. We got this series AGES ago (thank goodness because it's very hard to find now) and we got super sucked into watching it. It shows two very different (but in my mind, equally lovable) military figures. One is a beautiful, ambitious Germanic blonde dude, Reinhard (anime loves those) and the other is brilliant-strategist-but-humble-everyman Yang Wen-Li. They are rivals, but both sympathetic. There are also a zillion other characters. Character development and intrigue up the wazoo, lots of space battles...
Except, we never FINISHED watching it because we started getting intimidated by knowing the ending would be gloriously tragic and have us holding each other and sobbing. So this summer we decided to start again, and finish this time. I've got the tissues ready!!
So then we watched Gundam. Lots of Gundam. The original Gundam, Zeta Gundam, Double Zeta, Gundam Seed, Gundam 00, and Unicorn. My favorites were definitely the first two series. Classics! The formula is not too far off from Legend of Galactic Heroes: everyman versus beautiful blonde dude, complicated politics, and space battles. But Gundam has more female characters, including mecha pilots...it seems so strange to me that in Japanese 80s cartoons women actually got to fly around in robots, even, whereas in the States we pretty much got pink princesses. Gundam is also a little less heavy...although, yes, people still die and I still cried.
Now we're watching the new remake of Space Battleship Yamato. It's still coming out, but OMG, so good. I never saw the original or the old US version Starblazers, but the new one, at least, is a little more focused on the entire crew than the previously mentioned shows and there is more of a sense or urgency because they have to save Earth, and as the Starblazers theme song so clunkily suggested, "If we don't in just one year, Mother Earth will disappear." (Makes "Fighting evil by moonlight, winning love by daylight" sound downright elegant.)
The thing I love about all these shows is how multifaceted they are, and how they have plenty to appeal to both genders. It isn't just about having strong female characters (of which some of these stories are better than others), but about telling a story in a way that combines action, intrigue, drama, romance, humor, little tiny quiet moments and big heavy ones, complicated and lovable characters... Boy, I'd be a happy girl if I could capture all of that in one story.
In the meantime, it's good material for filling the well, and if you're an anime or space opera fan (I really can't say sci-fi...despite space and some telepathy, these are really stories about politics and war, with occasionally some uncomfortable parallels to real life!) I highly recommend any of them!