eMoods, a mood tracker for bipolar disorder.
DBT 911, an on-hand refresher of DBT skills.
Cognitive Diary, a diary and tracker for thoughts, beliefs, and behaviors.
SamApp, a stress and anxiety tracker, with useful self-help tips.
The Worry Box, an anxiety self-help app.
Cognitive Diary, a self-help app using CBT.
Depression CBT, a depression self-help app using CBT.
And, just as a fun added bonus:
My Calendar, a very useful period tracker app with options for PMS symptoms, intercourse (protected or unprotected), and a pregnancy mode.
All of these apps were selected and tried by yours truly.