My system has 1280×1024 screen resolution. In my system my design is looking good. But in other systems like 1024×768 screen resolution the design is looking bad.
Why do
This is the issue with web design - it's not page layout. If that's what you want, make PDF files.
While developing, you need to understand during the process what the screen resolutions you intend to support - basically the min and max height and width and check them during development, not after you have it looking good at one resolution.
There are tools like the web developer plugin for firefox which will let you quickly resize your browser to common resolutions to help you test.
https://addons.mozilla.org/en-US/firefox/addon/web-developer/
However, there is no "magic cure" to a design that looks bad at other resolutions. You have to understand how the browser will re-flow your design as the resolution changes.
Again, I must stress that you check the design in different resolution browsers frequently throughout the design process, not just at the end.
You can either choose to use liquid/fluid layouts, or you set a base resolution for the "lowest common denominator" when it comes to your clients viewing your site. Right now it's still 1024x768.
I personally don't think anyone is still "really" using 800x600, and if they are, I don't support them