Well you already have GitS: Stand Alone Complex, and both series (plus the movie Solid State Society) are great, and I think are an excellent series to get you into it.
Darker Than Black - Secret societies hiring assassins and mercenaries with special powers. Great characters, great story and it doesn't take itself too seriously.
Code Geass - It has mechs, but they are not so much the focus as the world war based around a futuristic feudal system, a man with the ability to have any command obeyed and a storyline that gets more extreme with every episode.
Fullmetal Alchemist Brotherhood - One of the best overall casts of anime characters ever. Hell, the chances are you will even like most of the bad guys. It's a pretty long series, but it will go very fast. It's based around two brothers who are trying to regain their normal bodies back after an experiment gone wrong. All the while a war is brewing due to a conspiracy at the head of the countries military.
Mardock Scramble - A young woman survives an attempted murder, only to be saved thanks to a life preservation technology known as Scramble 09. With a body that gives her the ability to control any electronic object, as well as an AI companion who has the power to take almost any form, she seeks revenge and justice.
Shows that I recommend, although the action isn't the main focus:
Puella Magi Madoka Magica - Is just a fantastic anime. If you google it and see pictures you will probably wonder how on earth it could be, but I don't want to give spoilers. Just make sure to watch at least the first three episodes before writing it off.
The Melancholy of Haruhi Suzumiya - A sarcastic high school student meets a girl called Haruhi Suzumiya who claims to only have interest in aliens, time travellers and people with special powers. Sounds crazy, but then she starts a club in order to find them. Sounds even crazier, but then unbeknownst to her, the three members who join her club happen to be an alien, a time traveller and a person with ESP, all who claim that she has willed them into existence.
There are many more I could recommend, but some of them may seem very strange to anybody unused to anime conventions. If you do decide you want to try any and all that may be good, here are some others:
Ergo Proxy
Death Note
Neon Genesis Evangelion
K-On!
Spice and Wolf
Angel Beats!
Elfen Lied
Gantz
Texhnolyze
Heaven's Memo Pad
Devil May Cry
Highschool of the Dead (May want to avoid if you despise pointless boob/ass shots)
Witchblade (May want to avoid if you despise pointless boob/ass shots)