Short answer: The Nintendo 2DS and 3DS play the exact same games. That includes games bought at retail, and games/demos downloaded from the Nintendo 3DS eShop.
Long answer: The Nintendo 2DS more or less has the same guts as the Nintendo 3DS, barring two major exceptions. First, the 2DS cannot project 3D images. That means the 3D capabilities that make the Nintendo 3DS so famous (or infamous, depending on your viewpoint), are not available.
Note that "projecting 3D" refers to the Nintendo 3DS's glasses-free 3D effect. The Nintendo 2DS can play games that have polygon-based 3D graphics. In fact, the Nintendo 2DS can play the Nintendo 3DS's entire library. That includes all upcoming 3DS games.
The second major difference between the 2DS and 3DS is the 2DS's lack of stereo sound. It has one speaker. Of course, if you plug in headphones, you get stereo sound.
Otherwise, all differences between the 2DS and 3DS are aesthetic and monetary. The 2DS is cheaper than the 3DS, costs less, and resembles a tablet instead of a clamshell.