There are several key differences between LCD and plasma screens and CRTs. Both types actually contain two glass screens -- a front screen, which is what you look at, and a rear screen, which is part of the process of generating the images displayed on the front screen. If either screen breaks, the TV won't work.
LCD and plasma screens use flat sheets of glass, rather than tubes like those used in CRTs. They don't have the structural strength of a curved piece of glass. They're also much thinner. Plasma TVs have screen thicknesses of less than 2 mm [source: Panasonic]. Are they more fragile than CRTs? We didn't have the heart to smash anyone's high-definition TV to find out, but logic would suggest that yes, these types of screens are more susceptible to damage. In addition, there's plenty of evidence on the Internet of people who have cracked the screens on their plasma or LCD TVs with an inadvertantly hurled Wii Remote.
As to the question of whether or not they can be dislodged from their display stands more easily, we again turn to common sense in the absence of experimental evidence that could only be obtained by knocking a bunch of nice TVs off their stands. Lighter objects slide more easily than heavy ones of the same general profile. Plasma and LCD TVs actually have a smaller profile -- less of their bottom surface is in contact with the stand below them, so there's less friction to keep them in place. Also, as LCD and plasma TVs get bigger, they don't get thicker. That means that a very large screen TV will be tall but thin, an inherently unstable form factor. For larger TVs, most manufacturers include straps and screws to secure the TV directly to the stand and the wall behind it for exactly this reason.
Just like CRTs, newer types of TVs have many sensitive electronic components. It's even possible to damage an LCD screen in such a way that it still works, but there are "dead pixels," regions of the screen that no longer function and stay black. All types of TVs carry and store a lot of electricity when they're operating -- when something goes wrong, occasionally there can be a large discharge of energy. This can result in a burning smell or even smoke, but it's rare for a TV to actually catch fire due to a malfunction.
For more information on high-definition televisions and related technologies, smash your way over to the next page.