My kids watch it from time to time, but i think they have heard me say how stupid the show is so many times that they actually are starting to believe me or see it for themselves . Both my boys are intellegent for their ages.
All my children that were young enough to watch Spongebob. Did and they were bright students. One was a straight A student. So I do not take studies seriously. My 2 and a half year old watches it today, he loves it and he is already learning his abc"s, counts to 11, knows his colors, knows his shapes, knows his vehicles and if you ask him to pick out a certain amount of something he will only pick out said amount. I feel that kids are only dumb because we make them that way. There are worse shows example adventure time is very violent, Dragon ball z is same, ect.
It's absolutely forbidden in my house. I didn't even know they'd done studies on Spongebob but I already felt it encouraged children to be stupid and act stupid. My kids watch shows like Dora the Explorer (my 3 year old already knows more spanish than I do!), Super Why (my three year old has her ABC's almost down, she still skips J and N and has trouble remembering H when she sees it), and Caillou which teaches manners and patience. I love these three shows. I briefly let my kids watch Rugrats until my 3 year old kept saying "stupid" and "dumb" which are no no words in our house.
To give you an example. My now 9 year old SD was allowed to watch whatever she wanted up until the age of 5 (when I said I didn't want to ever hear or see Spongebob or Fairly Odd Parents, or iCarly on TV again). She couldn't read before then, she knew her alaphbet song...but didn't recognize the letters except those in her first name (which she could write), she had trouble counting. My two and three year old can already count to 15 and on a good day my 3 year old can count all the way to 30...though she still says twenty-ten after twenty-nine about half the time. So it's a combination of the parents working with the kids and the parents not allowing their children to watch shows that encourage stupidity over other more desirable traits like being problem solvers.