If you can't find a single solvent that you can crystallize your product from, mixed solvents can be very useful. There are two ways to do it - one is like Herrhanson described. You find one solvent that your compound is very soluble in, and another one that it isn't. Then you dissolve your compound in a small amount of the soluble solvent, and add a large amount of the insoluble solvent. Your compound will "crash" out of the solution - it rapidly forms a precipitate which can (hopefully) be filtered off. (This technique is usually referred to as "precipitation" rather than "recrystallization" and although very rapid and quite useful, does not exclude impurities in the same way that recrystallization does).
Another way is to dissolve your compound in a small amount of the soluble solvent heated to its boiling point. Then you add your insoluble solvent slowly while keeping the solution hot, until you just see your solution start to get turbid (you get areas that are slightly more opaque or milky, right at the limit of solubility of your compound in the mixed solvent system). Then you add a drop more of your soluble solvent to make it all clear again, and let it cool slowly. If you are lucky, you will have found the perfect solvent for growing nice large crystals of your compound.
Ethanol/water is a particularly useful solvent system, because it acts more like a non-polar solvent when it is hot, and more like a polar solvent when it is cold. Compounds which dissolve well in ethanol but not in water can usually be nicely crystallized from this mixed solvent system.
This is a good description of these methods, though I do not advise crashing out my product. If I did, I'd probably skip recrystallizing it.
Back to the original question, "When would you use mixed solvents?"
My answer, in every case I can. If time is important, you can change solubility faster by simply adding another solvent than evaporating a solvent. The description by fledarmus succeeds in describing this. In simple cases, you can recrystallize a sample in 10 minutes.
Let me go further in this. A recrystallization is an experiment. I actually prefer it to be the second trial in purification. I prefer to TLC my sample so I can have an idea of the type of impurities and crude amounts that may be present. If I have an impurity that is more polar than my product, then a solvent system like methanol or ethanol-water may be a good choice as the least polar compound can crystallize first and the more polar impurity remain in solution. Similarly, if the impurity is less polar, a mixture with hexane or similar are often better. In this case, the more polar product can crystallize first and the less polar impurity remain in solution. These are gross suggestions and TLC needn't predict actual solubility results.
If I have a compound that needs recrystallization, I like to begin with a solvent in which the compound can dissolve easily. If there are any impurities, it can often be recognized by the differential in dissolving. If the bulk of the sample dissolves and there is something that does not, the insoluble material is unlikely to be product. Filtration at this stage is much easier as crystallization is less likely to occur during the filtration to remove any impurities as the solution is less likely to be saturated. I prefer to use a low boiling solvent at this stage, dichloromethane with hexane or methanol with water. If I need to remove some solvent, this is often easier with a low boiling solvent.
I do not like to use a single solvent as it may require excessive solvent to dissolve a sample and if there are impurities, they can be difficult to distinguish from an insoluble product. Furthermore, because crystalline solids dissolve more slowly than oils, significant amounts of excess solvent are common. Bumping may also occur. This excess solvent further delays isolation of a crystallized product.
It is also important to note any cloudiness in a crystallization as noted by fledarmus. This is an impurity. If I am recrystallizing from CH2Cl2-hexane, I often use a small amount of silica. This is analogous to a charcoal treatment in ethanol-water. Charcoal pulls out the least polar from water and silica pulls out the most polar from hexane. If you are attempting to achieve high purity (not high yield), you may perform several filtrations.