Some file share resources, for example Mega(moderator edit), uses new approach (which is available in HTML5) to download files, they use sandboxed section of browser's local storage, files are downloaded in following sandboxed section's folder(s):
for Google Chrome:
C:\Users\[USERNAME]\AppData\Local\Google\Chrome\User Data\Default\File System
and for Opera:
C:\Users\[USERNAME]\AppData\Roaming\Opera Software\Opera Stable\File System
After that, browser pop-ups usual file download window and just copies file to download location, but file in File System folder stays there (without extension) and if do not delete them manually, file system folder can grow indefinitely depending how much such types of download is used.
Only App which I found can clean this automatically is HotCleaner but, it has to be installed as browser extension for individual browsers, it wold be nice if CCeaner had ability to clean File System
(Moderator edit: removed unneeded links. Judged Hotcleaner not to be a direct competition product, other moderators may over rule -nergal)