Salt in a pot of water I noticed that when I throw salt into a cooking pot and then mix, the salt collects in the center. As salt is denser than water, I would have expected it to go towards the border of the pot, and not in the middle. What is going on exactly there?
 A: Replace the salt with tea leaves, and you'll find the answer... with wikipedia.
The tea leaf paradox is exactly what you describe: denser than water particles accumulate in the vortex center.
This is an indirect effect of the pressure gradient cited by philip_0008. As you stir, the liquid accumulates at the periphery so that the extra height generates a radial pressure gradient that exactly balances the centrifugal momentum. As I explain in my answer to philip, this is however not sufficient to prevent particles from going outwards (and actually they transiently do so). 
However, a secondary flow is generated because of the wall friction on the liquid, which reduces its outward motion close to the bottom wall, see the wikipedia sketch:

This secondary flow entrains the particles along the bottom wall, dominating over their centrifugal momentum, but cannot entrain them upwards in the center of the vortex against their weight, hence their accumulation in the center.
A: One candidate for a force that will oppose the particle's inertia is the so-called inertial lift that is created in the neighbourhood of the wall: grossly speaking, the flow created around the particle interacts with the wall and pushes the particle away from it. 
You can see this paper: http://www.pnas.org/content/104/48/18892
...but it will not dominate at the scale and distance from the wall in your home-experiment, see my other newer answer!
A: I've actually tried it when I was younger, intentionally stirring water circularly very fast in a large basin, such as to make a large 'vortex', and noticed that everything that I put in goes toward the center. 
The reason seems to be that:
From wikipedia: "The fluid motion in a vortex creates a dynamic pressure (in addition to any hydrostatic pressure) that is lowest in the core region, closest to the axis, and increases as one moves away from it, in accordance with Bernoulli's Principle."
So that any object will have higher pressure at the side facing away from the center, than the side facing the center, thus there is a net pressure toward the center. Similar to how airplanes fly due to the pressure difference at the wings.
