CRT's ,Projectors and plasma screens are vulnerable to image burn. LCD's do but it takes much longer to burn in (a few weeks), but it doesn't harm to have a screen saver on.
Wiki: Plasma displays are highly susceptible to burn-in, while LCD-type displays are generally less so. Because of the more rapid luminance degradation of current organic compounds used in OLED-type displays, OLED is even more susceptible to burn-in than plasma. In addition, the wide variation in luminance degradation with OLED will cause noticeable color drift over time (where one of the red-green-blue colors becomes more prominent).
In the case of LCDs, the mechanics of burn-in are different than plasma and OLED, which develop burn-in from luminance degradation of the light-emitting pixels. For LCDs, burn-in develops in some cases because pixels permanently lose their ability to return to their relaxed state after a continued static usage profile. In more typical usage profiles this image persistence in LCD is only transient.
Screensavers derive their name from their original purpose, which was an active method of attempting to stave off screen burn. By ensuring that no pixel or group of pixels was left displaying a static image for extended periods of time.
Other source: A common question asked is if alternate, non phosphor based television products, such as LCD and DLP televisions, are susceptible to burn in. The most common answer given to this question is no, LCD and DLP televisions are immune to burn in.
It's generally accepted that DLP TVs are generally immune to burn in. For LCDs, however, immunity is somewhat of a half-truth.
In my own opinion i would say that LCD's don't have this image burn problem