The standard venus flytrap can only shut and reopen 10 times in total. It doesn't really "spring" shut; it takes anywhere from 5-15 seconds for a venus flytrap to close (amended: apparently, the literature says that a flytrap shuts in a second or less. Perhaps this is true in nature, but I've tripped venus flytraps before, and you could definitely watch them shut. My friends and I never got our fingers stuck. I don't know why some researchers had to video tape a fly trap shutting. FYI, this was in a botanical garden and they were small flytraps. Anyway, they shut b/c cells on the outer layer of the plant expand, which pushes the trap shut. This is also related to why it can only shut a set number of times.). Once it closes around a victim, the flytrap exudes digestive enzymes to kill the fly and break down the nutrients so the nutrients can be absorbed into the plant.
Also, venus flytraps don't need flies to live. They normally grow in nitrogen-deficient soil, so they're carnivorous for added nutrients. However, if grown in properly fertilized soil, they'll do just fine without meat.
There are also many other kinds of carnivorous plants, including bladder worts, pitcher plants, etc. Check it out.
More information can be found at "Barry's Carnivorous Plant Page."