It looks like the iPad mini's constrained supply has finally caught up to the high demand. The device is now showing as "In Stock" in most countries around the world, showing that Apple's supply has either increased to meet the high demand, or the high demand has dropped off slightly.
In all reality, it's probably the latter option. People are probably seeing the rumors of a new iPhone 5S and are starting to think that an updated iPad mini could also be just around the corner. There have also been rumors of an iPad mini with Retina display coming soon and this could be contributing to a decrease in demand.
European customers are still seeing 1-3 days as the quoted shipping time, but those should soon change to "In Stock." If you want to pick up a new iPad mini, now is definitely a good time as you shouldn't have to wait for them to ship out.