One eye is definitely dominant, but both work. They just don't work together; I'm reasonably sure that the right eye is being suppressed when both are open. I can see the difference between my left and right eye by closing each in turn, but I can't merge the two images into a 3D picture of the world. I rely entirely on knowing the size and shape of objects (the monitor is rectangular, and how trapezoidal it looks tells me how far off straight it is), and on occlusion of one object by another (I'll sometimes catch myself moving my head slightly, or more than slightly, to make that happen). Friends have commented that I have a habit of bumping into things when walking - but I'm fine at driving. No, really! :) And I suck at catching, although that might just be a Slashdotter thing...
I only discovered that I had no proper 3D when I was specifically tested for it as part of a pre-employment medical. Of course, this came as something of a surprise to me, given that I'd been landing planes quite happily for ten years (which came as something of a surprise to the doctor), although thinking back to my training, I can see how it wouldn't be an issue. I was taught to look for the runway to be a certain 2D shape on approach, symmetrical with a given height:width ratio, and for the flare and touchdown all I had to do was look at the far end.
So yes, I have ways to cope, but I don't have 3D vision in the conventional sense, and a doctor can prove it.
Except in the cinema... which I find intriguing. And I do see the subtle 3D, not just the in-your-face 3D (which I really hate, because it completely destroys my immersion in the story just to make me feel like the extra two bucks were worth it....grrrr....). Clearly I can still do it, and all the relevant hardware and software does work. Just not in the real world.