Do catalysts undergo physical changes during a reaction?
I'll just give an example of a catalysis to show you that catalysts do really temporarily react with the starting product and eventually will be regenerated after the catalytic reaction. 

An example is the catalytic decomposition of formic acid to carbon monoxide and water by using sulfuric acid as a catalyst. The sulfuric acid donates one proton ($\ce{H+}$ ion) which is then bonded to the central carbon atom in the formic acid molecule. Then next another hydrogen atom from the sulfuric acid reacts with the hydroxyl group present on the formic acid molecule to yield water. In the end the sulphate ion snatches the last two present hydrogen atoms from the formic acid molecule and yields carbon monoxide. The sulfuric acid is regenerated.

$\ce{HCOOH + H2SO4 -&gt; H2COOH + HSO4- -&gt; H2CO + SO4^{2-} + H2O -&gt; CO + H2SO4}$

So catalysts do undergo chemical changes in the catalytic reaction but are regenerated after the catalytic reaction is finished.

This means that if you are using a catalyst, you can normally reuse it after your catalytic reaction because it has the same chemical (and physical) properties as before the catalytic reaction.

Also : when you use manganese dioxide as a catalyst to decompose hydrogen peroxide, you will see that the black solid compound is the same after the catalytic reaction.

There are also so called 'sacrificial catalysts' (which aren't regenerated and do physically/chemically change, but aren't real catalysts) -> see http://en.wikipedia.org/wiki/Catalytic_cycle