GolfScript (31 25 chars)
..[10base{.{+}*+(\}@*]?0>
Input as an integer on top of the stack. Output is 0 (false) or 1 (true). Online demo which lists the Keith numbers up to 100.
..[10base{.{+}*+(\}@*]?0>
Input as an integer on top of the stack. Output is 0 (false) or 1 (true). Online demo which lists the Keith numbers up to 100.