The Swedish authority for Universities (VHS) is investigating how to introduce application and tuition fees for Non EU students. It looks like students applying in 2010 will pay an application fee, and full fees will be introduced in 2011. The current information in Swedish says that tuition fees will be introduced for those students starting their education in the Autumn 2011. Thus, apply in 2010, you will be paying fees in 2011 – though we must wait for the governments investigation , results on the 15th September.
Malmö university has more on this here: http://www.mah.se/english/News/News-2009/Application-fee-for-foreign-students—Autumn-Term-2010/
The governments decision can be read here (in Swedish): http://www.regeringen.se/content/1/c6/12/80/04/bd2a502b.pdf