There are more people in the US involved in alternative health than ever before. The following list is of things that have at least some solid research support according to the National Center for Complementary and Alternative Medicine (US regulating agency).

Mild Depression
St John's Wort
S-Adenosyl-L-Methionine (SAMe)

Sleep Problems
Melatonin
Valerian

Anxiety
Valerian
Kava
Acupuncture