Do they only prevent the screen from being burned in or do they save power, too?
Some recommendations from Wade Hampton: Screensavers usually display graphics, look for ETI, or perform other tasks. When using your screensaver in this manner, you may actually consume MORE power. For example a computer using XSETI as a screensaver might get far warmer (hence use more power) than when it was being used to edit a document or perform a compile.
Some screen saver programs:
The purpose of xscreensaver is to display pretty pictures on your screen when it is not in use, in keeping with the philosophy that unattended monitors should always be doing something interesting, just like they do in the movies. The benefit that this program has over the combination of the xlock and xautolock programs is the ease with which new graphics hacks can be installed: you don't need to recompile this program to add a new display mode, you just change some resource settings. Any program which can be invoked in such a way that it draws on the root window of the screen can now be used as a screensaver without modification. The programs that are being run as screensavers don't need to have any special knowledge about what it means to be a screensaver.
LockVC is a console-locking-program combined with a starfield screensaver. Executing LOCKVC on a virtual console brings up a starfield that starts to rotate around all three axes.
To really save power, and if your X server plus monitor supports it, use the dpms option of xset (see the manual page for xset). For example, to enable the DPMS (Energy Star) features of you X server: xset +dpms
You may also manually change the mode of your X display:
xset dpms force standby xset dpms force suspend xset dpms force off
Note that suspend and off usually save much more energy than just standby, especially in CRT displays.
According to manufacturers, switching off LCD displays more often doesn't reduce their lifetime. As user can easily notice, there is no significant penalty either between suspend and off modes in terms of switching on time.
In modern graphical desktop environments (like Gnome and KDE), it is easy to configure automatic display switch off after a given inactivity timeout:
KDE display power management: configure it in Control Center -> Peripherals -> Display -> Power Control.
Gnome display power management: configure it in Desktop -> Preferences -> Screensaver -> AdvancedControl Center -> Peripherals -> Display -> Power Control.
AFAIK a CRT consumes on the order of 25 percent more power when displaying a plain white screen than displaying a plain black screen. So, a screensaver that's mostly black can help save power, even if it doesn't actually use DPMS to power down the screen. Of course, one that's very bright and colourful, or that keeps the CPU running fast is not much help.