--for those who speak English as their second language or who just want to improve their writing
(Illustrated version of Quirks of English)
Continual means proceeding seemingly without interruption; an action frequently or closely repeated with little or no time between. The use of continual is restricted "to what occurs regularly or frequently in a prolonged and closely spaced series." Continual denotes "a close and unbroken succession of things, rather than absolute continuity, but it implies repetition with occasional interruptions."1
Continuous means "proceeding in space or time without interruption; unceasing, constant, protracted; extending without irregularity."1 The use of continuous "denotes that the continuity or union of parts is absolute and uninterrupted."1
1From Hypertext Webster Gateway: Webster's Revised Unabridged Dictionary (1913) and WordNet 1.6.