I can, at will, cause either one of my eyes to break convergence and look somewhere else and then alternate which eye is lazy by "looking" out the other eye. That "lazy" eye will then start looking outward and I'll get double vision, but how noticable it is depends on how out-of-whack my eye convergence is (I can also control how much convergence I loose, so I can go from slight, almost overlapping double vision, to nearly completely different viewpoints). If I'm looking at something to the extreme right or left I usually end up looking with just one eye, but I don't notice the double-vision for some reason. I've since learned to physically turn my head / body towards what I'm looking at since that makes it physically possible for me to look at something with both eyes. Another trick I use is to look at something with my "outside eye" (i.e. if I'm looking at something to my right, I will look at it with my left eye, visa-versa if looking left). I'm not sure if that makes sense to anyone, but AFAIK, most people should be able to "look" through either of their eyes at will. Over time, I've managed to adapt my behaviour so that most of the time these symptoms don't occur.
The most dangerous downsides to all this is that when I get extremely tired, or very drunk, I can no longer keep my eyes converged and normal vision becomes impossible. Nothing short of intensely focusing on a high-contrast area (say, the sharp edge of a table) will bring convergence back. However, I'm not sure if this happens because of my lazy eyes, or if it happens to other people. Driving while tired is extremely dangerous for me, especially at night, since I loose all sense of depth perception when I get double-vision and I suddenly have no idea which lane I'm in or where I'm headed.
One interesting aspect about all this is that if I cover one eye then I can no longer get this behaviour to happen, which has saved me a few times during extremely boring lectures! Something about looking with both eyes causes the trouble.