They certainly can - and they're also more susceptible to burn if you do any gaming or watch the same channels all the time with logos. LCD's are not prone to this. From a wear standpoint, plasmas are similar to CRT's. LCD's will go until they burn out.
Bryan
Plasma used to be prone to burn in... but virtually every unit out there now (the panasonic industrial models being an exception I can think of off the top of my head) have an orbiting or anti-burn in circuit. Some dim the tv if a static image is placed up there for extended periods of time. Most have an orbit or pixel shift circuit. At a defined interval, the circuit shifts the image a pixel or two so that it doesn't burn in. It works exceptionally well. I had a Toshiba plasma that I ran 15 hours a day for nearly two years that didn't have a hint of burn in and it spent most of the time displaying a static computer desktop.
plasma does dim over time.... but almost all models on the market right now have a half life of 60,000 hours. That means that the plasma will be half as bright as it was when you first turned it on after 60,000 hours of use. Given how bright most plasma panels are, while it will be noticable, that's still a very bright panel even at half brightness.
Based on what's on the market right now, plasma still has the advantage on ansii contrast and true on/off contrast. LCD has come a LONG way, but it still isn't as good. In dark movies, plasma is going to win. In mixed content scenes, plasma is going to win. Plasma isn't as precise/sharp on defined computer desktop resolutions because of the nature of the pixel structure. A lot of plasmas have limits on the desktop resolutions they will support. Plasma has the advantage on response time. LCD doesn't use as much power. Most LCDs won't generate as much heat as an equivalent sized plasma (especially if you turn the backlight down on the LCD). On most sizes, you can get higher resolution for less money with LCD. But if you can live with a 768P panel, 50 inch plasmas are going to be cheaper than 50 inch LCDs... LCD uses a more non-reflective surface than the glass in a plasma. So LCD isn't as prone to reflection problems in highly lit rooms. I've had about equal reliability rates with both technologies... neither of them are as good as CRT based tubes.