As per research, the following are the most used aspect ratios for laptop/desktop displays:

Aspect ratio (Lowest) Resolution to test on
16:9 1280×720
16:10 1280×800
4:3 800×600

 

These are the lowest band screen resolutions of the displays that would be used while practicing web applications. We need not test on the screen having the upper resolution of same aspect ratio cause it would validate for the screen having higher resolutions with same aspect ratio assuming relative units are used for text size, images and other elements of HTML.

 

Thus, validated screen resolutions will be:

Lowest resolution Resolutions that would be valid
1280×720 1366×768, 1600×900, 1920×1080, 2560×1440,  3840×2160 and on…
1280×800 1440×900, 1680×1050, 1920×1200, 2560×1600 and on…
800×600 960×720, 1024×768, 1280×960, 1400×1050, 1440×1080, 1600×1200, 1856×1392, 1920×1440, 2048×1536 and on…

 

There is also a web application to test a web application’s responsiveness.
http://quirktools.com/screenfly/