If you find you can't uninstall the average application - a browser, say, graphics editor or word processor - then it's a nuisance, but no more. Windows and the rest of your software will probably go on working just as it always did.
If the uninstall fails for an antivirus tool, though, it's a different story. Security software makes many low-level changes to your PC, and if these can't be undone then your PC may become unstable, or behave unpredictably. Worse still, you may find you can't install any new security software because it detects the remnants of your old package, and demands that be removed first.
There's a simple solution to these problems, though - and it's called AppRemover. Run the program, choose the option to look for failed uninstalls, and it'll scan your Registry and hard drive looking for remnants of old security packages. Hundreds of packages are supported, from all the major security companies: AVG, Avira, F-Secure, Kaspersky, Lavasoft, McAfee, Microsoft, Panda, PC Tools, Symantec, and many more. The chances are it'll detect what's left of your security program, then, and you can have it removed in a couple of clicks.
Note that AppRemover 3.0 is now Windows 8 compatible. It also includes a toolbar option which you can choose not to install, during installation.