I was using it without any problem in LinuxMint 8 but it has not been easy with 9. First, I was happy to see it included among the programs in Software Manager so I tried to install it from there. Nada. I mean, after installation, Dropbox appeared in the Menu list under Internet but each time I would click it, a small window opens saying it's installing Dropbox but it never actually finishes. The window just disappears.
Next I went to the Dropbox site itself and downloaded it from there directly. Installed it and the installation window said it installed. I clicked on the icon and a downloading window appeared. It finished downloading but then nothing significant happened after. I still couldn't open Dropbox.
This time I tried to be smarter and checked the forums and I quote below the SOLUTION I found. It also explains it much better and in a shorter way.
The Mint version of Dropbox, despite the high scores in the community website, is buggy and not worth keeping since it constantly goes through this install loop everytime you reboot your computer. I encountered this annoyance in Helena and it wasn't fixed in Isadora. I suggest you completely remove it, delete the hidden configuration files/folders and download/install the .deb installer from the official Dropbox site itself.
Note what Pilosopong Tasyo (it's his reply up there) says about completely removing configuration files/folders. You can do this by seeing them in the first place. I mean you won't see them unless you open your home folder, click Edit, click Preferences, then click the phrase that says show hidden files or something similar.
If you wish, you can check out the entire exchange of ideas here: http://forums.linuxmint.com/viewtopic.php?f=47&t=48675&p=280851&hilit=dropbox#p280851