Liselotte Frisk, a researcher at dalarna University, in collaboration with the Christian newspaper Dagen, a few years ago conducted a survey of Swedes' attitudes towards different alternative beliefs. The project has a few years on its neck and some material has been removed from today's website.

Of the more than 900 respondents, 32.8 percent said they fully or partially agree with the statement "I believe that man is reborn (reincarnation)". When similar questions have been asked in the past, about 25% agreed. Among those under the age of 24, the proportion who believe in rebirth is a whody 42.2 percent. (From The Day, 2008-07-16)

http://www.dagen.se/var-tredje-svensk-tror-p%C3%A5-%C3%A5terf%C3%B6delse-1.186792
Chart presenting the results of the survey (Day, 2008):