The standard venus flytrap can only shut and reopen 10 times in total. It doesn't really "spring" shut; it takes a half second or maybe a little more. 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."
cross-posted to HeardSaid