I haven't had my property go vacant yet (fingers crossed). I've worked very hard to find renters while the property is still occupied. Aside from the income that I miss out on if the property goes vacant, I've also found that rentlal units show better when furnished -- rooms look much smaller without a couch or bed in them for scale.
I also have a clause in my lease that prevents tenants from moving out during the winter months, a time when it would be much more difficult to find new tenants quickly.
I advertise on Craig's list, the housing website for my local university, my local newspaper (print and online), and also have a sign out front with flyers. I've pasted flyers up around the neighborhood as well.
When I've been showing the property, if people aren't biting, I simply lower the price until it goes. If the unit rents for $1000 a month, missing a month's rent is the same as lowering the rent by $85, over the span of a year.
I've written an article about advertising and finding tenants on my website: http://www.iboughtaduplex.com/?p=13