What is the difference between synchronous generator & asynchronous generator?

A synchronous generator is called “synchronous” because the waveform of the generated voltage is synchronized with the rotation of the generator. Each peak of the sinusoidal waveform corresponds to a physical position of the rotor. The frequency is exactly determined by the formula f = RPM x p /120 where f is the frequency (Hz), RPM is the rotor speed (revolutions per minute) and p is the number of poles formed by the stator windings. A synchronous generator is essentially the same machine as a synchronous motor. The magnetic field of the rotor is supplied by direct current or permanent magnets. The output frequency of an asynchronous generator is slightly (usually about2 or3%) lower than the frequency calculated from f = RPM x p /120. If the RPM is held constant, the frequency varies depending on the power level. The peaks of the waveform have no fixed relationship with the rotor position. An asynchronous generator is essentially the same machine as an asynchronous or induction motor. The magnetic field of the rotor is supplied by the stator through electromagnetic induction. The output frequency of a synchronous generator can be more easily regulated to remain at a constant value. Synchronous generators (large ones at least) are more efficient than asynchronous generators. Synchronous generators can more easily accommodate load power factor variations. Synchronous generators can be started by supplying the rotor field excitation from a battery. Permanent magnet synchronous generators require no rotor field excitation. The construction of asynchronous generators is less complicated than the construction of synchronous generators. Asynchronous generators require no brushes and thus no brush maintenance. Asynchronous generators require relatively complicated electronic controllers. They are usually not started without an energized connection to an electric power grid, unless they are designed to work with a battery bank energy storage system. With an asynchronous generator and an electronic controller, the speed of the generator can be allowed to vary with the speed of the wind. The cost and performance of such a system is generally more attractive than the alternative systems using a synchronous generator

Well I have read all the answers ! very good opinions by all experts , But i will add an answer , if someone is being asked this question in a paper or interview , for students and fresh engineers :

Synchronous Generator : in this type the rotor speed is just equal to the flux produce by the stator .

Asynchronous or Induction : in this type Rotor speed is not equal the Flux produced by the stator .

A synchronous generator rotates an electromagnet within coils generating three- phase alternating current. All by itself, it is not "synchronized" with anything.I parallel the four machines, and the induction motor begins spinning the propeller at a speed less than synchronous speed -- say,3200 rpm. The induction motor is acting as an asynchronous motor. Suddenly, the wind picks up big time, and the propeller, instead of taking energy, begins pumping mechanical energy into the motor. Now the speed is4000 rpm, and the induction motor is now acting as an asynchronous generator.

Asynchronous machines act like a donkey following a carrot, there's a phase shift between the speed of rotor and the speed of the rotating magnetic field. In synchronous machines, there's no phase shift, the speed of the rotor is called synchronous speed.

synchronous Gen.  no a phase shift between the speed of rotor and the speed of the rotating magnetic field, although it in Asynchronous Gen. 

1. An induction or asynchronous generator is an electric induction motor driven at speeds above its synchronous speed.
2. It has a solid armature, or squirrel cage, that is an electrical short circuit. When the current is connected, the machine will start turning like a motor at a speed that is just slightly below the synchronous speed of the rotating magnetic field from the stator. If we manually drive this rotor at exactly the synchronous speed of the generator (1800,3600 RPM etc.), the magnetic field rotates at exactly the same speed as the rotor, we see no induction phenomena in the rotor, and it will not interact with the stator. If we increase speed above the synchronous speed of the generator, the rotor moves faster than the rotating magnetic field of the stator, and the stator induces a current in the rotor. The more mechanical power that is delivered to the rotor, the more power will be transferred as an electromagnetic force to the stator, and in turn converted to electricity, which is fed into the electric grid. 
3. Because most single stage steam turbines develop their peak efficiencies between3600 and5500 RPM, the 2- pole (3600 RPM) induction generatorallows for a direct drive application, eliminating the need for a speed reduction gear and a costly lubrication system, as the turbine is usually ring lubricated and the generator has grease packed ball bearings.
4. A synchronous generator runs at a constant speed and draws its excitation from a power source, external to, or independent of, the load or transmission network it is supplying. A synchronous generator has an exciter that enables the synchronous generator to produce its own "reactive" power and to also regulate its voltage.  Synchronous generators can operate in parallel with the utility, or in "stand-alone" or "island" mode. Synchronous generators in the <15 mw power range are only available as4-pole (1800 RPM) units, are almost always geared, and require large pressure lube systems. 

• In a synchronous generator, the waveform of generated voltage is synchronized with (directly corresponds to) the rotor speed. The frequency of output can be given as f = N * P / 120 Hz. where N is speed of the rotor in rpm and P is number of poles.In case of inductions generators, the output voltage frequency is regulated by the power system to which the induction generator is connected. If induction generator is supplying a standalone load, the output frequency will be slightly lower (by 2 or 3%) that calculated from the formula f = N * P / 120.
• Separate DC excitation system is required in an alternator (synchronous generator).Induction generator takes reactive power from the power system for field excitation. If an induction generator is meant to supply a standalone load, a capacitor bank needs to be connected to supply reactive power.
• Construction of induction generator is less complicated as it does not require brushes and slip ring arrangement. Brushes are required in synchronous generator to supply DC voltage to the rotor for excitation.