You can, but only if you leave a static image on the screen for a very long time, crt monitors are less prone but Plasma screens suffer badly from it. Hope that helps.
monitors that have phosphors in them are susceptable. this means CRT screens, and the much newer and not-yet-released SED displays. LCD and plasmas are generally fine for this, but some occurances have been known.
My office has Acer 1714 LCD screens which are all 9 months old and they ALL have screen burn - the imprint of the internet explorer bar at the top can be seen on the a blank desk top. I didn't realise it could happen to LCD's.
it doesn't happen for the same technical reason, but it can still happen (as you have experienced); however, it takes longer for it to happen than a crt.
whatever monitor you're using, you're still best off setting the monitor to turn off after 5minutes of idle time.