It all depends on the type of anemone and how sensitive you are.
If you are allergic to bee or insect stings, then be VERY careful when handling anemones as their toxins can trigger the same allergic reaction that a bee sting will cause...which is potentially fatal.
Some people are just more sensitive than others. You actually get stung every time you touch one, just that most of the time the stinging cells do not penetrate far enough into your skin to cause any harm. Sometimes you will get a little reaction (red bumps). Either way, you should wash your hands really well after handling them before you touch your eyes or mouth as those surfaces are far more sensitive.
Should you feel a stinging or burning after touching one, rinse the affected area off with vinegar before using water. the vinegar will neutralize the toxins and stop any more damage from occuring. Then rinse with soap and water.
Hope this answers your questions.
-The Grog, M.D.