Q:

How much does the resolution affect performance? 

If you take a generic game and change resolution to 640 x 480, 1280 x 1024 and 1920 x 1080 respectively, how heavily would this affect performance? 
Is resolution an important factor or rather neglectible when trying to find perfect settings for a non-high-end graphics-card? 

A:

It is (after switching AA off) the most important setting: doubling your resolution requires four times as many pixels to be updated per frame.  So, as a rough estimate, by decreasing your resolution for a factor 1/f, your framerate can increase up to f².