based on the year of publication in the U.S. Basically, any characters that appeared in publications prior to 1923 are PD in the U.S. The Strange Case of Dr. Jekyll and Mr. Hyde was first published in 1886 and has therefore fallen through the public domain trapdoor (along with the characters within the covers). Sir Arthur Conan Doyle's characters appeared in approximately 50 stories published before 1923, and 10 stories afterwards. In the case you mentioned, Doyle's estate argued that the "whole character" was not formed until the final post-1922 work was published. The Seventh Circuit court of Appeals disagreed and held that the Holmes character who appeared before 1923 is PD -- so, you're free to copy him and Watson. But the remaining 10 works are still protected and you cannot use elements from these works -- for example, you can't reference the fact that Watson had a second wife. (Here's a summary of Sherlock's copyright history.)
BTW Dept ... If you're looking for more match-ups between public domain characters check out this site or this one.