Inositol

Inositol is chemically similar to glucose (the type of sugar required by the brain for energy). It is a precursor in a so-called "second messenger system," which cells require to communicate with each other. In the brain, these second messenger systems are activated by various neurotransmitters including serotonin. There is some evidence that brain levels of inositol are reduced in depression and anxiety disorders. Inositol is present in a typical diet, in amounts of about 1 gram per day. Doses of supplemental inositol are typically 10-20 grams per day.

A Cochrane review from 2004 concluded that there was no clear evidence of supplemental inositol being beneficial in the treatment of depression:
http://www.ncbi.nlm.nih.gov/pubmed/15106232

Here's a 2006 reference from Bipolar Disorders showing that supplemental inositol could help treat bipolar depression in some patients already taking lithium or valproate. In 4 out of 9 patients taking 6-20 grams per day of inositol, their depression substantially improved over 6 weeks, with continuing improvement over an additional 8 weeks. However, the other 5 out of 9 patients either did not improve, or actually had worse symptoms. The patients who got worse had more manic or irritable symptoms at the beginning of the trial. When the results were averaged, the inositol did not appear to help significantly--however, it is notable that a subgroup of patients appeared to benefit significantly.
http://www.ncbi.nlm.nih.gov/pubmed/16542187

This 2001 study from the Journal of Clinical Psychopharmacology compared 1 month of inositol (up to 18 grams per day) with fluvoxamine (up to 150 mg per day) in the treatment of panic disorder. Both groups improved similarly. The fluvoxamine group had more side effects of tiredness and nausea. The study is limited by its short duration.
http://www.ncbi.nlm.nih.gov/pubmed/11386498

This 1995 study from the American Journal of Psychiatry compared 12 grams per day of inositol with placebo, for one month, in the treatment of panic disorder. The authors conclude that inositol was effective with no significant side effects. Mind you, when eyeballing the chart of data from individual patients, the results did not look very impressive.
http://www.ncbi.nlm.nih.gov/pubmed/7793450

Here's a negative study, showing no difference between inositol and placebo, when added to antidepressant therapy for OCD:
http://www.ncbi.nlm.nih.gov/pubmed/11281989

The same author as above published a study in 1996 showing that inositol on its own was superior to placebo for OCD treatment. However, despite "statistical significance" being found, eyeballing the data from each patient (presented in the body of the paper) reveals doubtful clinical significance (that is, the amount of benefit looked quite unimpressive to me):
http://www.ncbi.nlm.nih.gov/pubmed/8780431

Here's a reference to a 2001 study showing that inositol was superior to placebo in treating binge eating and bulimic symptoms. In this case, I found the data to be clinically significant. However, the study was limited by its small size.
http://www.ncbi.nlm.nih.gov/pubmed/11262515

Here's a small 1995 study showing that 4weeks of inositol (12 grams per day) was superior to placebo in treating depressive symptoms. The data appeared clinically significant, though modest.
http://www.ncbi.nlm.nih.gov/pubmed/7726322

Here's a 2004 reference from a dermatology journal showing that inositol supplementation led to improvement of psoriasis in patients taking lithium:
http://www.ncbi.nlm.nih.gov/pubmed/15149510

In conclusion, inositol may be modestly effective for treating anxiety, eating disorder, and depressive symptoms. It may perhaps be quite variable in its effectiveness, i.e. some individuals might have much more benefit than others. It appears to be well-tolerated with few side-effects. I could not find good data on long-term safety though. The quality of the evidence is not very robust-- the studies have involved only small numbers of patients, for short periods of time. More research is needed.