If I buy a 1920x1200 monitor (16/10), can I play in 1680x1050 (16/10) resolution without losing image quality since the ratio is the same?
If there is drop in quality, is that serious? If I use, say, 1280x1024 resolution with my current 1680x1050 monitor, it's very blurred and ugly.
I'm just wondering that if I move to 24"+ monitor do I need to upgrade my video card from HD 5870 Vapor-X, because I can't play in 1680 then I need to upgrade. I'd like to play BF3 when it comes out with maxed out GFX
Yea, you will lose image quality as you have reduced the graphics. That is pretty much the only drop in quality you will see. You may also see black bars around the sides of your screen if you lower them to a certain extent, as your monitor wont be able to display such low graphics over the extent of the entire screen.
As nadim said, you'll lose image quality. Running 1680x1050 on a 1920x1200 screen is just like having a screen that can only display 1680x1050. Less pixels means a less-sharp image. Go down even further to, say 960x600, and the picture is even worse. The lower the resolution, the more pixelated the picture looks. It'll still fill the whole screen if your monitor or GPU has a scaler, but it will look worse. There's no reason you can't use a 16:9 (1920x1080) or even 4:3 (1600x1200) resolution either, but they will either be stretched, which looks horrible, or you will have black bars. Anytime you choose a lower resolution it looks worse.
It's also the case that any monitor not running at it's native resolution will look very slightly worse than one running at it's native resolution, so a 1920x1200 22'' monitor running at 1680x1050 would look worse than a 22'' 1680x1050 monitor running at the same resolution. The 22'' 1920x1200 monitor would obviously look better at 1920x1200 than the 22'' 1680x1050 one does at 1680x1050 though. (They don't make 22'' 1920x1200 monitors anymore, but a few companies did in the past, and it works as an example.)