After almost three years of renovations the Helsinki Natural History Museum re-opened its doors in May 2008. The museum has free entry on Thursday afternoons between 16 and 18 which we decided to take advantage of. It is housed in a 1913-built building originally used as a Russian school, then as a the Finnish Officer Cadet School, before taken over by the University of Helsinki and used as a museum. The English wikipedia page is a bit short, but the Finnish page has more information.
From my childhood I mainly remember the impressive stairs, and the two-headed calf. They're both still there!