LCD displays can have this problem. It stands out a bit more on an LCD projector but it can still happen to standard screens. Plasma displays have this problem, only much worse. They can have burn-in after 15 minutes in the worst cases.
The best solution if you have to leave an image up 24/7 is to go with a CRT or a DLP projector.
EDIT: Here's a quote from an NEC white paper...
"There are many concerns with both LCD and plasma displays when using a static image. LCDs can exhibit a phenomenon known as ?image retention.? Image retention is caused by a pixel being in the ?on? state for an extended period of time, causing a small charge to remain in the cell in the ?off? state, similar to a memory effect. However, this phenomenon is not permanent. To reduce the chance of this phenomenon, many advances have been made in the liquid crystal material itself, and the display may include a ?screen saver? pixel-shifting technology to further reduce the risk.
Plasma displays use phosphor and can suffer from phosphor burn-in just like CRT products that use phosphor. Although some manufacturers include pixel-shifting technologies to reduce the chance of this happening, the end result is permanent. When phosphor burn-in occurs, the phosphor material is damaged and this cannot be removed.
The amount of time required for both image retention and phosphor burn-in is almost impossible to calculate because of all the variables involved. The color of the image, the pattern, the display?s brightness setting and many other factors can affect the time before these phenomenons appear."
