In their second paper on the structure of DNA*, Watson and Crick (pdf) described how DNA's structure suggests a pattern for replication:
"…prior to duplication the hydrogen bonds are broken, and the two chains unwind and separate. Each chain then acts as a template for the formation onto itself of a new companion chain, so that eventually we shall have two pairs of chains, where we only had one before." - Watson and Crick, 1953
This is called semiconservative replication.
Today we know that this is the pattern used by living cells, but the experimental evidence in support of semiconservative replication was not published until 1958. In the 5 years between Watson and Crick's suggestion and the definitive experiment, semiconservative replication was controversial and other patterns were considered.