There was actually a study published recently where researchers (perhaps grad students) tickled various primates and recorded the sounds they made. When they compared the sounds made by the various primates (including humans), they saw that the similarities matched up well with the evolutionary relationships of the species of primate (i.e. species that were more closely related genetically made similar sounding laughs). The paper can be found below along with a link to a podcast discussing the research. Also, below is a link to a Radio Lab podcast discussing the science of laughter. In it, they talk to researchers who suggests that rat may display laughing behavior.
Davilla Ross M, Owren MJ, Zimmermann E. Reconstructing the Evolution of Laughter in Great Apes and Humans.
Current Biology (2009)
doi:10.1016/j.cub.2009.05.028
http://www.sciencefriday.com/program/archives/200906054
http://blogs.wnyc.org/radiolab/2008/02/25/laughter/