I'm thinking of buying a 21:9 aspect ratio monitor because I do a lot of work editing documents and the super widescreen would be very helpful for that. Since I also intend to use this monitor with my PS3, I'm wondering how the PS3 handles 21:9 displays (in this case, 2,560 x 1,080 resolution). Are the games letter-boxed? I assume the PS3 is incapable of actually outputting games at such a resolution (my Google search revealed only unsubstantiated rumors).
It's not up to the PS3, it's up to the monitor. The PS3 can't "handle" 21:9 in any way, it'll just output at 1080p (or 720p/480 whatever) like it always does, which will only ever look right at 16:9.
21:9 monitors like the Philips Cinema 21:9 TV should all have display modes for 16:9 1080p display, which will pillarbox 1080p content and show it at it's native resolution in the center of the screen.
If for some reason your monitor didn't pillarbox it would likely be stretched out. It's a feature you'll have to check out on the display side, not the console side.