Space Battleship Yamato.
It's an old anime from the 70's, it has a 2010 remake and a 1977 movie if you're short in time; there are quite a few good sequels and remakes of this series, so it should last for a while. It's a little hard to find (search for space battleship yamato 1974 or star blazers) but it should be worth it.
If you like watching shows about surviving against impossible odds against superior firepower, technology and numbers through wits, balls, risks, improvisation and sheer willpower, this will be more than awesome - in the series, mankind is on the brink of destruction after a war with aliens, and as their last hope, they actually RESURRECT the Yamato battleship (yes, THAT Yamato, the largest battleship ever). Just so you don't think it's another glorious war anime, this one is pretty serious while still being awesome - there are quite a lot of personal themes in this anime about loss, taking risks, moving on and living to fight another day - while watching, you never once feel that their task will be anything close to easy, and it makes it that much better.
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