Recent? Or biggest hitters?
I'd say Time is running out, Hysteria, Stockholm Syndrome, Supermassive Black Hole, Starlight and Knights of Cydonia are the pick from the last two albums.
Earlier stuff would be Plug in Baby (By far the most popular) and New Born.
Oo and Citizen Erased. In a word they're phenomenal.
:EDIT: Try to get some live stuff if you can too, makes you appreciate it SO much more as they're playing the songs as they were intended.
Also look up the live vidoes on youtube as I've found the visual element to be a very strong part of the performance.
Sorry I couldn't keep it to a couple of songs but there are quite a lot of equally popular ones. For the most popular go with Supermassive Black Hole, Plug in Baby, Stockholm Syndrome and Hysteria.