How many mains frequencies are there?
For a detailed list of utility frequencies, see this article from Wikipedia.

The frequency of mains electricity is strongly related to the rotational speed of the machines used to generate it (usually alternators connected to some form of turbines). That's why frequencies are somewhat lowish. 

The world has somewhat standardized, along the way, on 50Hz/60Hz systems (with most of the world using 50Hz). Some higher frequency are indeed used (e.g. 400Hz), but the main problem with them is they cause more problems when transmitted over long lines. Therefore they are used when their advantages are paramount, e.g. when space is limited (aircrafts, submarines, etc.), because higher mains frequency means, for example, more efficient and less bulky transformers.

Some relevant excerpts from the Wikipedia article (emphasis mine):


  Several factors influence the choice of frequency in an AC system. Lighting, motors, transformers, generators and transmission lines all have characteristics which depend on the power frequency. All of these factors interact and make selection of a power frequency a matter of considerable importance. The best frequency is a compromise between contradictory requirements.


[...]


  There is a fixed relationship between the number of magnetic poles in the induction motor field, the frequency of the alternating current, and the rotation speed; so, a given standard speed limits the choice of frequency (and the reverse).Once AC electric motors became common, it was important to standardize frequency for compatibility with the customer's equipment.


[...]


  Since, for a given power level, the dimensions of a transformer are roughly inversely proportional to frequency, a system with many transformers would be more economical at a higher frequency.
  
  Electric power transmission over long lines favors lower frequencies. The effects of the distributed capacitance and inductance of the line are less at low frequency.
  
  Generators can only be interconnected to operate in parallel if they are of the same frequency and wave-shape. By standardizing the frequency used, generators in a geographic area can be interconnected in a grid, providing reliability and cost savings.


As for the "how do they sound like part", the usual frequencies lie in the audible spectrum, therefore google for a free signal generator program to run on your PC. Your sound card is well able to generate sounds at those frequencies. Remember to set the generator to produce a sine wave, since that's the waveform of mains voltage. Different waveforms will sound different.