In metals the number of free charge carriers is constant. As the temperature goes up their mobility goes down. Because the carriers can't move as much there is higher resistance.
In semiconductors the number of charge carriers increase exponentially with temperature and this overrides the decrease in mobility.
It turns out that we're lucky. Semiconductors have a complex behavior over a wide range of temperatures. It just so happens that they behave like useful semiconductors at temperatures that we're accustomed to on Earth.
EDIT: I should have said that conductivity is a function of the number of free charge carriers multiplied by their mobility. If the number of carriers increases faster than the decrease in mobility then conductivity can increase with temperature.
If a device's resistance goes down with temperature then we say that it has a negative temperature coefficient. This is not necessarily directly related to the conductivity of the device's material makeup. Other physical processes can affect the temperature coefficient.
Some things that have negative coefficients:
-light bulbs
-diodes
-bipolar junction transistors
Some things that have positive coefficients:
-metal wires
-Field effect transistors