Actually most duplicate file finders are able to find all kinds of duplicate files as they are comparing the binary contents of the files. So even if you do not have a specific scenario like mouser's example, you may be able to free a lot of disk space by just cleaning your music collection, picture collection or download folder from duplicate files. It is important to note that although you will have duplicate files in other directories like your Windows or Program Files directory, most of them are needed by these programs and your system - so you should never scan your complete hard disk and delete all duplicates you can find.
mouser's example of downloading files and adding them to your collection is something DoubleKiller Pro can handle much better than other duplicate file finders: As you can see in brotherS' screenshot of the Scan Options page, there are two separate directory lists that perfectly suit this task. By adding the directory of new files to the upper list and your collection to the second one, DoubleKiller Pro scans the new files for duplicates and also checks if any of the new files is already contained in your collection. Imagine you have a collection of 10,000 wallpapers, just stumbled upon a new site and downloaded 100 wallpapers from it. Other duplicate file finders like NoClone would have to check all 10,100 files for duplicates while DoubleKiller Pro would only compare the 100 files against themselves and against the collection, which is obviously much faster.
DoubleKiller Pro also beats the competition in other tasks, like scanning MP3 files for duplicates: Using the advanced content comparison options, you can compare the MP3 files against each other without regarding the information about song and album title, composer and so on (so-called ID3 tags). This way DoubleKiller Pro will also find MP3 files that have exactly the same MP3 content, but a differently spelled or omitted album title. (Details are described in the usage examples chapter of the help file.)