I'm not familiar with Origin's DRM (or the one that will be used on the next SimCity), but if I got the game, would I and my girlfriend be able to play it at the same time, each on their own computer at home, or would we need two separate Origin accounts and buy the game twice?
With Origin, you can install as many copies as you like. But when you start the game, you need to log in Origin. You cannot login at two different computers at the same time.
If you are playing and your girlfriend logs in, you will be put in offline mode. It seems like you have to be online to play the game. See this link.
No - it will not be possible for you to play SimCity twice with a single account. In order for you to both be able to play at the same time you will each need your own Origin account and your own copy of SimCity. This was confirmed during a Reddit AMA with a Maxis employee where it was stated that if you lose your internet connection during gameplay, you will not immediately be disconnected but if you don't re-establish a connection you will be kicked out of your current game:
We will allow you to play for as long as we can preserve your game state. This will most likely be minutes.
In addition, it is highly likely that features such as the Global Market and trading within multi-city regions will require a persistent internet connection to function properly.
As far as I know you cannot be logged to the same Origin account twice, nor playing the same game (bought only once) together.
Otherwise we could build up a legit sharing community where we buy a copy and share account infos to play together with a minimal expense! :)
So, answering your question, if you want 2 people to play a game you need 2 Origin accounts and therefore 2 bought copies of the game itself.