We find screens of varying sizes in use these days. In fact we might be browsing content not only on laptop or desktop but also on mobile or iPad or other handheld devices. You'll come across different resolutions too. 1280x800 is being widely used, still 1024x768 remains most common. In fact these days higher reolutions like 1440x900, 1680x1050 and 1920x1080 used increasingly day by day. So we need to take care of most of the resolutions while designing. Site should not look weird with change of resolution or screen size. Since 4:3 is no more a baseline of aspect ratio now website should look descent in other aspect ratios too....check your site on 16:9 aspect ratio for verifying with higher end.
Use fluid/liquid layouts i.e. the content flows to the width of the browser window. While designing the page fixed layout may look easier as well as impressive. But take into consideration that not all the users will be viewing the page in same window width. This invites the trouble of repeated scrolling and makes it cumbersome to read. If you have to continuously scroll left and right would you continue being on that site....Obviously not, unless and until your content has some great pulling factor! Using table for placing images and text is good approach. You can assign it the width as percentage of window width (Yes there are advantages of fixed width tables like you can ensure that nothing gets distorted. Relative height,width helps in fluid layout if height to width ratio of image is not a matter of concern.)
Finally before launching don't forget to test your web pages on various browsers, window sizes as well as various platforms. Enjoy all-compatible website designing!