Death to Creepers!
Minecraft is a deceptively complex program. Whenever an update is released, the ‘download’ page on Minecraft.net, a new minecraft.exe file is available for download. This file replaces the previous version, and, in most circumstances, replacement of this file is enough to solve any problem that Minecraft might be having.
But this isn’t actually all there is to the program.
When Minecraft is run for the first time, it creates a hidden folder that stores all of its active files, including ‘save’ data and the like. If you are having problems with Minecraft that are NOT being solved by re-installing the Minecraft.exe, then it might be required to delete this hidden folder and most/all of its contents. If you go into your ‘Search’ tool and search for the file ‘minecraft.jar,’ you should be able to find the hidden folder with relative ease. However, if the search function doesn’t find it, the folder’s default address is: C:\Users\Your_Username\AppData\Roaming\.minecraft
Deleting this entire folder deletes Minecraft PERMANENTLY from your computer. Re-installation, however, is as simple as re-downloading the ‘Minecraft.exe’ file from Minecraft.net, and running it the same way you would run the game. It automatically reinstalls the necessary files in the proper location. If you wish to save any current single-player worlds you may be working on, back-up the ‘Saves’ folder before you delete the .minecraft folder.
This process should not effect your multiplayer save-data in any way: as far as I know, save data is stored on the server, not on your individual computers.
Hope this helps.