Is there a free program to completely remove programs & destroy all traces?

Solution
The only program I have used for destroying things utterly (though manual) is called FileAssassin. It deletes anything no questions asked beyond "are you sure?" and does not care about access permissions either.

Note: this is very powerful in the sense it will ignore warnings about sensitive Windows files so you have to be certain you are not deleting something integral to your system.

Depending on what you're removing it may be a good idea to search for uninstallers made specifically for removing said program. As an example I had issues with iTunes not removing from my system entirely and used a utility called ByeTunes which existed for the sole purpose of removing iTunes program traces.
The only program I have used for destroying things utterly (though manual) is called FileAssassin. It deletes anything no questions asked beyond "are you sure?" and does not care about access permissions either.

Note: this is very powerful in the sense it will ignore warnings about sensitive Windows files so you have to be certain you are not deleting something integral to your system.

Depending on what you're removing it may be a good idea to search for uninstallers made specifically for removing said program. As an example I had issues with iTunes not removing from my system entirely and used a utility called ByeTunes which existed for the sole purpose of removing iTunes program traces.
 
Solution

Powerful tools will have powerful interfaces.

I do something simpler. Having run Windows for a long time I know what my permanent Apps are, so after installing OS and those Apps and everything seems to run perfect, I do an OS Image Backup. Hence anything I install afterwards and don't like, I simply restore this backup and I know I go back EXACTLY as it was before and whatever crap I installed afterwards never happened, including a few trial-wares. This is also a quick and effective way to de-malware.
 


FileAssassin is very user friendly, it even adds the option to delete files on the right click menu. If you're familiar with using the delete function by right click then you can use FileAssassin no problem.

What are you trying remove exactly?