How to change user without closing applications running?

Solution 1:

In Preferences under Accounts > "Login Options" you can enable fast user switching by selecting the "Show fast user switching menu as: [Icon, Name, Short name]". After that you should see an user menu on the menubar. Just select "Login window" and you'll be able to login as another user without logging out.

Solution 2:

The answer for command-line based enabling of switching is also quite relevant. Posting here as a cross-reference.