A cracked foundation is nothing to be sneezed at. This is the kind of problem that goes directly to the heart of the structural integrity of your home. If you have a sizable crack in your foundation, you need professional opinions and help when fixing it. There are a few methods that may be employed, depending on what the professionals recommend.
The First Step
Instead of calling contractors to compare prices immediately, you may consider having a structural engineer look at the damage. This is someone with specific expertise in these matters who is not going to try and sell you any kind of service after identifying the problem. A structural engineer can draw up plans for the repair of your foundation, which you can then, in turn, give to the contractor you've hired to take care of the situation.
Simple Fills
Some repairs may be done by a contractor chiseling the crack wider and applying hydraulic cement to the gap. As it dries, the cement will expand and make a tight seal. This may not last forever though; water will still be able to get halfway into the foundation, and, over time, can wear away the repair.
Another agent used to fill in foundation cracks is urethane foam. This is injected into the damaged area, and can reach the very back of the damage, providing a more complete fill. Some experts may recommend this repair, which is relatively simple and quick.
Excavation
Certain damage may require that the foundation wall be excavated from the outside by using large construction equipment. This would take a few days to completed and be much more expensive than the options above. However, these decisions are most certainly the prerogative of the experts, and the life of your house (and even the people living in it) depends on this repair being done properly.
Remember: if you see a crack in your foundation, you'll want to get it taken care of as soon as possible. The damage will worsen with time and only become more dangerous and expensive to fix. That's not to mention the flooding and other problems it can cause. Leave this one up to the pros, but make sure that you are getting the best help you can.