In reply to Dispater:
Depends very much on species, which in turn varies by location.
For identification, likely harm and treatment etc for Irish sea species see the Ecojel guide at
http://www.jellyfish.ie/
Lion's Mane jellyfish are the usual ones that cause noticeable stings for swimmers. Contact with the 'tentacles' can happen without actually seeing the jellyfish e.g. on kayak paddles or fishing line. I usually get stung many times through a summer/autumn season but it's rarely enough to be a problem. It generally feels like a nettle rash in intensity and duration of tingling / pain. Scrape the stingers off with a credit card or rinse with lots of salt water. For Lions Mane stings DO NOT try using urine, vinegar, fresh water etc as these can make the stingers release more of the irritant chemicals. Can be an issue for dogs too, because they tend to see the red jellyfish on the beach and try to eat them, thinking they are some sort of meat, and get a very sore mouth / throat.
More serious stings come from "non-Jellyfish" species, mainly Portuguese Man-o'war, and can be dangerous because the pain can be severe enough to make it difficult to keep swimming - a kid I was in school with nearly died after jumping off a jetty on top of one.