The AppleVis iOS App Hall of Fame http://www.applevis.com/apps/hall-of-fame is a showcase of great apps that are fully accessible to VoiceOver users.

Best Android apps for the blind and visually impaired from Android Authority, an independent online publication that is a voice for the world of Android & technology: http://www.androidauthority.com/best-android-apps-visually-impaired-blind-97471/

American Foundation for the Blind, a national nonprofit expanding possibilities for Americans living with vision loss, has a list of Android apps: https://www.afb.org/afbpress/pub.asp?DocID=aw170208