Annika is a surprise hit of recent years, inspired by golfer Sorenstam; for Trekkies, it was also the name of a 'Star Trek:Voyager' character. Some people's first memory of it might be as Pippi Longstocking's friend. A nice namesake for an ancestral Ann.
Annika Settergren, a character in the "Pippi Longstocking" books
Annika Giannini, character in The Millennium Series by Stieg Larsson
Human given name of Seven of Nine, former Borg character on "Star Trek: Voyager" Princess Annika, main character in Barbie's Magic of the Pegasus
Annika, from the movie "Laggies"
Annika Berglund, character from The dung-beetle flies at dusk, by Maria Gripe