UPDATE: There are several, better alternatives to Airdroid now. However, it seems most Linux distros are now working with MTP fairly well. I know in my experience, Mint (Ubuntu based) works out of the box, as does Manjaro (Arch based). If it doesn't work out of the box or natively, then be sure to search your package manager for an MTP solution.
Newer versions of Android mount storage as an MTP device instead of mass storage. The benefit to this is simultaneous access on the Android device and the PC. Unfortunately, while Windows supports it natively just fine, linux solutions are fairly buggy as of right now.
Currently, the most reliable (and it still is a little flaky to get going, but once connected is fine) that I have found is go-mtpfs. Here is a link to help you get it set up. You have to mount/dismount from command line. There is also a unity launcher in that thread if you're on Ubuntu unity, however.
The best option, though, unless you are transferring a lot of data, is to use something like AirDroid. It is a free app in the play store for local network transfers, and provides a web interface to use with your computer's browser. It even provides a drag and drop file interface, as well as even allowing access for sms messaging, call logs, app installs, and many other things.