Based on what the posters have recommended in this thread and you wanting to watch more serious sci fi shows, i would suggest the following Appleseed Appleseed Ex Machina Vexille Macross Zero Sentou Yousei Yukikaze Starship Troopers: Invasion These are the type of Japanese anime shows that you might enjoy.
I just realized that no one has recommended Black Lagoon. Seriously? It has gun-running nuns, psycho paramilitary maids, a flame-scarred female Russian mob boss, an island paradise populated almost entirely by violent criminals and a smuggling operation that uses a WW2 patrol torpedo boat as transport. How do you not say "Everybody needs to see this series at least once!"?
Black Lagoon was frakkin' awesome! I saw it last year/earlier this year and it totally rocked from beginning to end! The main characters were all cool and crazy in their own ways.
^^^See? It's official! If you haven't seen Black Lagoon yet you have to go see it! Right Now! Stop readin' this and go download it or somethin'!
True, it is totally badass. I would have got to it, pretty quickly if I had continued listing all my favorites. Speaking of... Looks like we finally get the OVA over here. Also to steer this back to Forbin's question, you should also check out the works of the independent studio Rika/Directions, for some short but great science fiction. They have done Time of Eve which will be available with English sub and dub internationally this year or next thanks to a bunch of fans contributing to their Kickstarter project. They have also done an OVA version of Time of Eve, and a few other short mini-series like Pale Cocoon, Aquatic Language, and their most project, Patema Inverted.
I haven't seen Black Lagoon, but I would recommend Jormungand in its place (since it's something I watched) if I had to come up with a show in its genre.
Apologies for the necro, but this seems like the logical place to mention this; Anime Ltd have launched a kickstarter to get Mai Mai Miracle released on blu ray in the UK and US. Original target was $30k which they blitzed inside 24 hours. They're onto the stretch goals now - the first of which is an English dub. Details; Mai Mai Miracle