The taskbar has been completely redesigned in Windows 7, so that only one icon for any application will ever be active. I do not believe that the behaviour of XP that you are used to can be replicated in W7 -- although I have noticed that some software will continue to have multiple active icons if multiple instances of it are running at the same time.
Concerning internet browsers, the various tabs for web pages that you have opened are typically located near the top of the browser window, so that you may simply need to change your habits of controlling the various open web sites from the taskbar to the browser tabs.
If you are using Firefox, it is very easy for it to be poorly configured, so that it opens web pages in new windows rather than new tabs -- and these windows can be hard to navigate in W7.
In Firefox, clicking on Tools, then Options will provide you with the means to change the behaviour of your browser.