At some point the B-word inevitably comes up when programmers are gossiping about their jobs. Everyone has a story about hitting the wall. I've had some burnout-like symptoms over the years, too. The biggest one for me is the feeling of writer's block, where I just can't even bring myself to get started on my list of things to do.
The only remedy I've found is to build whatever I'm curiously thinking about in the back of my mind. This has been a wide range of things: drawing schematics of physical computers; writing a window-manager; reimplementing protocol buffers from scratch; visualizing a bug tracker as a burn down chart; configuring incremental backups; load-testing something; etc.
The key part of it is no matter what deadlines I have or pressure I'm under, I throw away my cares and just write some code. I try to be happy right now. I scratch my own itch. Once I do that the juices are flowing and soon after I can get to work. Unlike other advice I've seen, I don't try to avoid programming to overcome burnout. I do the opposite. I overcome burnout by doing something that lets me remember how much I enjoy writing code.