Can you damage a monitor by running it above the recommended resolution

what monitor is this?

It won't hurt anything but when you run higher resolution than your monitor supports it averages the display down to that. In other words, you're not getting any benefit runnint it 1920x1080. It is still only diaplaying 1600x800. If you set it to the recommended resolution it may run faster too.

your LCD monitor has a fixed number of pixels . In your case 1600 x 800 [ or is that 900? ]
If you run it at 1080p resolution you achieve nothing but create a slightly fuzzy image as the monitor tries to compensate for the incorrect input

It should be ok because if it can display a picture @ 1920x1080 without loss of the signal its fine, it may be the case though in that mode the image does not fit the whole of the screen, the Hz factor of the monitor not being high enough for the resolution will be the cause.
The only time you can mess a monitor up for example is if it is the old 15Khz to 25Khz scanning frequency. If you put 31Khz through it, then it would damage the screen.
Anyway most new monitors handle 31Khz and above to cope without breaking.

it is a samsung syncmaster 2033sw

thats 1600x900.

Well, I have a Samsung SA300. When I 'forced' it to get 1080p, battlefiled 3 would flash a blurry stripe in the middle of it.

That was all.

click on desktop. go to screen resolution. find detect or identify.... or click on resolution to see recommended. run it at that.

Yes to swifty, and run bf3 at that resolution, too. It will run much better.

i'am using it for my 360 and ps3 occasionally when i stop playback on a bluray dvd and if I leave it alone for a while is turns to rainbow colored static then my ps3 either reboots or the monitor reboots and then it is fine again I'm not sure how to switch the resolution back to 1600 by 900 my ps3 display setting don't give me an option to and the monitor message that says its not optimal mode doesnt let me change it either

People always try weird stuff with hardware.. Keep it simple and run it at native resolution