“Riders on the Storm” - The Doors
I would have to agree that a gift to your therapist is a bad idea. You really don’t want to do anything to blur that line of professionalism. However, I really like the theme of this mix anyway, so I’d like to add:
Crazy (A Suitable Case For Treatment) - Nazareth, from the Heavy Metal soundtrack.
Somebody’s Watching Me http://www.afn.org/~afn30091/songs/r/rockwell-somebodys.htm - Rockwell
There are also two albums I can think of:
The Crazy World of Arthur Brown - Arthur Brown
Music For Crazy People - Branford Marsalis (good luck finding this one)
Speaking of cant believe no one’s mentioned it:
“Crazy”, by Pink Floyd. Of course, one could mention literally half of their tracks from their Big 4. (DSOTM thru the Wall.)
Twilight Zone - Manhattan Transfer
**Twilight Zone ** (instrumental) - The Ventures
Also on the same album: Doctor Psyche, the Cut-rate Head Shrinker
Does he like dance music?
Insanity by Oceanic was a rave classic from 1991.
Frontier Psychiatrist - The Avalanches
Crazy on You - Heart
Psycho - The Sonics
Valid or Void - Shrink
While echoing the concerns of other posters, I hasten to add:
“What Do You Hear In These Sounds”, by Dar Williams.
Flagpole Sitta-- Harvey Danger
Is it possible that I’m the first to mention The Doors, “People Are Strange”?
If you really do it, I think you should include “Busted” by Matchbox20 then get all offended when s/he asks what it’s about. 
Another vote for “don’t actually give this to your shrink,” but I love song lists, so:
“Crazy” – Pylon. Better known as it was covered by R.E.M. (This is a different song from other songs with the same title by Patsy Cline, etc.) “Yo-Yo” by Pylon is also good for the mix.
“Lithium” and “Tourette’s” – Nirvana
“Too Much Paranoias” and “Uncontrollable Urge” – Devo
Slightly off-topic: “She Cracked” and “Hospital” by The Modern Lovers (narrator sings of suicidal girlfriend.) Similarly, “The Drugs Don’t Work” by The Verve.
If you want to scare your therapist, use “Help Me Somebody” and “The Jezebel Spirit” by David Byrne and Brian Eno…
I don’t think that I’ve seen: “Mama He’s Crazy” by the Judds.
“Doctor My Eyes” - Jackson Browne
Or you could go for the triple-play dance mix:
Insanity
Amnesia
Insomnia
You might want to check out some of the suggestions in this thread.
Oooh, that’s evil. 
“Doctor Worm” isn’t about insanity. It’s about an aspiring musician, and the stage name he hopes to use someday is “Dr. Worm”.
As for my suggestion: “Unwell” by Matchbox 20.
Psychosis Safari by The Eighties Matchbox B-Line Disaster. Chock full of headbanging goodness.