I never had a "normal" sense of humour and have been told numerous times that I've got "no sense of humour!". It's quite odd, because if I don't laugh at something other people find funny, they seem to take it deeply personally, as if I'd just insulted them.
As a child, other kids found me weird because I'd watch cartoons for the story, not the humour. I didn't even realise cartoons were supposed to be humourous until I was 11 when I was at a friends house watching cartoons, and ever other minute she and her 3 siblings would crack up and I'd have no idea why, so, to avoid being looked upon as "weird", I'd force a laugh and laugh along with them whenever they did.
Having said that, I'm currently obsessed with the Animaniacs, and I DO laugh at their jokes. Not so much the physical stuff, but the clever, witty remarks and puns that come from the Warners' mouths. Nobody understands what I see in the Animaniacs, but I don't understand what they all see in Family Guy or Southpark...