Overwrites unless the file is locked (ie. a .docx open in Word that two people are editing concurrently). If a file is locked you get multiple files with "(X's conflicted copy)" appended to their names
Although sometimes stuff is just gone and they're out of luck. I'm still not entirely sure what happens then, possibly a weird combination of everyone saving their project near closing time, the Internet connection maybe choking up a bit, and people shutting down their computer before everything is properly synced.
Dropbox is pretty good about never losing data. It can be suggested that this is one of the most interesting or valuable parts of its technology. Its practical use of bandwidth is another.