Are there any SLR digital cameras that you can take a picture using the lcd screen?

Just the one: the Olympus E330. Here's a review
http://www.dpreview.com/reviews/olympuse...
In effect, they took a perfectly good dSLR design and had the engeneering department beat it to within an inch of it's life to transform it into a point & shoot with interchangable lenses.

Yes, the Olympus is the only one so far.

It's been getting great reviews from the pros.

Yes, the Olympus has others have mentioned. That is a useful feature when the camera is mounted on a tripod, but otherwise breaks the basic rules of handholding technique. There are some accessories for other SLRs that attempt to do the same sort of thing for those tripod mount situations.

Vote for OMG's hilarious but 100% accurate answer.

Too true and too funny!