Trying out lighter Desktop Environments (LXDE, XFCE, etc.) is one way to go, and will probably yield the greatest noticeable difference in performance.
If, however, you are taken with Unity and want to stick with it, there are a few things you can do to speed things up a bit:
1) Choose "Unity 2D" at login instead of "Unity", if you don't mind going without desktop effects.
2) In Startup Applications, uncheck applications and processes that you don't need Ubuntu to automatically start for you at login (e.g. Bluetooth Manager if you don't have bluetooth, UbuntuOne if you don't use it, programs you simply don't use etc.) Before doing this, first make hidden startup applications visible in the manager:
sudo sed -i ‘s/NoDisplay=true/NoDisplay=false/g’ /etc/xdg/autostart/*.desktop
3) Install Preload, which detects the applications and processes you most frequently use and loads the binaries and dependencies for those applications ahead of time so they load faster:
sudo apt-get install preload
4) Make sure to update frequently. From time to time, it is also useful to remove .deb files and applications/libraries that are no longer necessary:
sudo apt-get autoclean