How can I securely erase files from a USB drive, using Windows?

CCleaner has an option to wipe free space on a drive.

Then there is also the free open source Eraser.

All of the other answers do provide ways to prevent the drive from being read using OS based recovery tools, however if the drive swapped out sectors due to bad sector errors/wear leveling (I doubt low end USB keys will do this but it is possible) the data could be recoverable by reading the flash memory chip directly and bypassing the controller.

See this answer from the security SE site for more details and read the Inaccessible media areas section on Wikipedia's "Data remanence" article. Once something has been written on any drive (flash/SSD/Spinning Disk) if you can not bypass the controller and write directly to the media (Even DBAN can not overwrite bad sectors) then you can not trust that the data is ever "gone".