You are probably very familiar with the character, and also with the phrase 'mad as a hatter.' The fact that hatters are associated with being crazy is not a coincidence. In the past, hatters would suffer crippling brain damage due to the mercury they used while making hats!
Hatters used mercury to turn fur into felt. During the process, they would inhale it. This had terrible mental and physical effects such as trembling, loss of coordination, slurred speech, loosening of teeth, memory loss, among others.
This was recently brought up again, during the time Johnny Depp was promoting the 2010 Disney version of the film. In the movie, the hatter always investigates things with the letter M, a reference to Mercury that the film played down.
As a bonus, check out this hilarious video from comedy group Derrick Comedy that parodies early century hatters. You might recognize one of the actors.