It is not completely true that all digital cameras have shutter lag. All point and shoot digital cameras do have some form of shutter lag, how long it is however varies greatly by camera and by manufacturer. On the other hand DSLR cameras have no perceptible shutter lag.
For instance, my wife's Canon PowerShot SX110 can take as much as 1 second to take a shot from the time the shutter is pressed. On the other hand my Canon EOS 50D in that same amount of time can take 5 shots. Now granted there is a more than 1k difference in price between these two cameras, but it does show the extreme difference between a point and shoot and a DSLR.
Many review websites have begun to post shutter lag data with their reviews as for many it is important. I know in my home my wife hates her SX110 simply due to the amount of shutter lag. So for the ultimate in lag less shooting the only real option is a DSLR.
Brian
"My father was very sure about certain matters pertaining to the universe. To him, all good things - trout as well as eternal salvation - come by grace and grace comes by art and art does not come easy." Norman Maclean, A River Runs Through It