Haven't seen these mentioned yet, and I recommend both:
Powergrid: Unique because there are no dice involved; a game of economics
Steam: Unique because there is a bank (partly tied to your score) that you can borrow against to build pieces faster
Powergrid: Unique because there are no dice involved; a game of economics
Steam: Unique because there is a bank (partly tied to your score) that you can borrow against to build pieces faster
edit: for what it's worth the game my wife and I end up playing most of the time when we have 45 minutes to kill is Carcassonne: Hunters and Gatherers, which isn't on the list.
Settlers of Catan can also work well for two people. You just have the two players control two colors each. This preserves the competition for resources needed to make the game fun.
Edit to add: Race for the Galaxy is also one of our favorites, but we've house-ruled it a bit so that the military strategy is not a guaranteed win.
It's the #6 game on BoardGameGeek [1], and well deserved to be there. Saying that "it's filled with math" doesn't make it sound all that exciting, but there's a good spacial element, an auction system that gets quite tense at times, and opportunity for "screw you" behavior that actually pays off. The winner is typically the one who was most efficient and has made some clever plays to keep his opponents out of his chosen markets.
How much of my hundred can I bid on this power plant? Well I need four oil this turn at what might be seven cost each, and I want to buy three houses at fifteen, so that means forty five plus twenty eight is seventy three, so I can spend up to twenty seven in this auction. There's no reason to force all that mental arithmetic, and it really sucks if someone loses because they missed carrying a digit mentally. Just use a calculator to abstract away the math and speed things up.