You can create a portable version of RStudio that will run on a USB drive. This allows you to run RStudio from any machine that has R already installed.
This allows RStudio to be portable, but your data and settings will remain on the local home directory of the computer.
On windows, you simply need to copy the RStudio directory (normally located in Program Files) onto your USB device. To open RStudio from this device, run rstudio.exe located in the bin folder.
Mac OS X:
For the Mac, after mounting the RStudio .dmg file, drag the RStudio Application file onto your USB device (normally you would drag this to your Applications Folder). To open RStudio from this device, simply double click the RStudio Application file from within your USB device.
Note that you may have to disable GateKeeper for the application to run correctly from the USB.
For Linux users, your USB drive must be formatted in a native Linux file format such as RiserFS or Ext 2/3. With this setup, simply copy the RStudio directory from /usr/lib onto the USB device. To open RStudio, run the rstudio executable file located in the bin directory of your USB drive.