Yes, burgers can be frozen either raw or cooked. Sometimes people even freeze raw hamburgers so they have time to congeal and are less likely to fall apart on the grill or to attempt killing some of the bacteria that could be on the meat after grinding.  You can also freeze a cooked burger. I suggest airtight plastic bags so you can get as much air out as possible. If you freeze a stack, separate them with parchment or wax paper. Freezing them individually makes for a simple meal for one in a jiffy!