The MOSFET can only carry positive current (n channel Mosfet, from drain to source).
If the load is inductive, there are times when the switch (MOSFET) must be on, but current flows in the oposite direction. The diode gives this current a path to flow.
If the diode is not used, the inductive current ceases instantly, generating high voltage peaks.
This figure shows the operation of the anti-parallel diode in a half-bridge inverter feeding an inductive load.
The left picture shows the state when the upper switch feeds the inductor. However when that switch turns off, inductor's current continues its path through the anti-parallel diode of the bottom switch (right picture).
Well, try to operate the inverter without those diodes and you should soon find out that you would be six transistors short (in a three phase inverter). Look here:
http://en.wikipedia.org/wiki/Flyback_diode
The german term is "Freilaufdiode," should you be interested.
an inductive current is not interruptible. You should reverse the voltage over the inductive load. Normally you can use any reverse diodes in a power circuit to reverse this voltage!
As you may see, not all IGBTs have this diode, usually high power devices bring it, from my point of view there are two main reasons: (i) IGBTs can block high voltage from collector to emitter, in the other polarity they can block few voltage before getting damaged, for example a 600V IGBT with no antiparallel diode can block around 15V from the emitter to collector the diode protects the IGBT from blocking negative voltage. (ii) Furthermore, power modules (IGBT plus diode) get a lot of practical application, for example in inverters where diodes are needed for freewheeling purposes, especially in voltage source inverters VSC, in current source inverters this diode is not necessary but another series diode is required. It depends on the application but the current marked is mainly focused in VSC and that is why they are so popular.
I think that in the process to bulid the MOSFET, the diode in anti-parallel in inherent to it, and therefore it can not be removed. In general, it is not a problem because you need this diode, as Iñigo Martínez de Alegria says, but in certain applications (some power supplies), you need to cancel this diode to aviod the effect of the reverse recovery effects in the switching by using a schottky diode and a fast recovery diode.
Any time you are switching an inductor, you need this diode called the SNUBBER. This is to prevent the inductor to generate a large negative voltage during negative current changes: V=LdI/dt. So, a large negative change in the inductor current will cause a large negative voltage, easily destroying any semiconductor in its way.
A motor is an inductive load, so, if you are using a half-bridge, or full-bridge, you need a SNUBBER DIODE. A reverse biased diode is always used (1N4148 etc ...) anti-parallel with the coil of a relay when you were designing it with a BJT, since BJT's don't have this reverse diode built-in. However, MOSFETs do ... In fact, you can't even get rid of it, like Salvador said. It is inherent in its design. Its positive effect is the fact that, it acts as a snubber ...and its free !!! Its negative effect is that, it is a pretty lousy diode : it has a pretty bad forward voltage (~1.6V) and it is slow. You need to use an additional Schottky in anti-parallel with the MOSFET in some power supplies, since you need a GOOD DIODE, not a SNUBBER ! (i.e., Vf=~0.4V etc ... with a fast response time).
Since most loads contain inductance, feedback rectifiers or antiparallel diodes are often connected across each semiconductor switch to provide a path for the peak inductive load current when the switch is turned off. The antiparallel diodes are somewhat similar to the freewheeling diodes used in AC/DC converter circuits.
It is necessary to add an anti−parallel or free−wheeling diode to obtain a fully functional switch. The IGBT cannot be connected in series with an inductor, a current source, or an open circuit, unless its snubber circuit is in use.
It should be mentioned here, that in SiC MOSFETs, a separate antiparallel diode is needed, as the intrinsic body diode of the SiC MOSFETs are unreliable. But in Si, Eamon is correct, the body diode provides suitable reverse current.
IGBTs do require antiparallel diodes as well, in both Si and SiC switches.
These diodes are there to provide a current path for the load, mainly if the AC side load has inductive characteristic (and they usually have some inductance from the connecting cables with self inductances). Such topologies are called “voltage source converters”. Another characteristic for these converters is the very low inductive paths connecting the DC side capacitor to the IGBTs and MOSFETs, in order to avoid/decrease/minimize overvoltages during switches turn on and turn off.
For RL loads, load current will not be in phase with load voltage and the diodes connected in antiparallel will allow the current to flow when the main devices are turned off.
This depends on type of application and subject. for power converters, it is used to help the passive elements such as inductor to discharge to allow next stage of conversion to start without reverse current.
It may also be used in some applications to protect IGBT or MOSFET but this is a different area to look at.
The backward connected diode has the function to clamp the reverse voltage of the transistor to the on voltage value of the diode. Also it makes the composite device reverse conducting. So, in many circuits these switching functions are required . As an example the inductive loads.
So there are two functions: protection function by reverse voltage clamping and current steering function by reverse conduction.
These provide return current path for the regenerative power produced by lagging load. For example, when the output voltage polarity is changed by triggering second pair of inverter(H-bridge) switches but the current polarity remains unchanged for a while due to load inductance , the current completes (returns) its path through the antiparallel diodes of previously conducting switches.