For those who are interested:
DSM-IV Asperger's Disorder
I'd hesitate to diagnose Frodo or Bilbo with Asperger's (regardless of the Ring-related issues which Leyrana Silumiel points out) simply because the diagnositc criteria refers to something which actually impairs social function, and if you look at Bilbo & Frodo's interactions with other hobbits as well as elves, men, etc, that impairment's not there. But I'm no psychiatrist.