Standard website works reasonably well in normal Android browser.
Dedicated application (with limited functionality): Your Move by Asim Pereira.
2. iPhone / iPad
Standard website works reasonably well in normal iOS browser. There is no dedicated application for this platform.
3. Windows Phone
Martin Benedik developed ICCF client for Windows Phone, which can be also used for SchemingMind (standard chess and chess960 games). See http://windowsphone.com/s?appid=323e590e-98e7-df11-9264-00237de2db9e.
4. Old devices
SchemingMind provides simplified web interface suitable for older mobile phones and PDAs. See this page for details.