Yeast Viability and vitality are related, but they are not the same. Yeast batches can be found with high levels of dead cells that still show very high fermentation performance (vitality, e.g., often with batches from fermentations with higher temperatures), as well as batches with very high viability but with very poor fermentation performance (e.g., storage of yeast for long times at very low temperatures).
The reference analysis for viability is the plate count measurement, which is not practical for the homebrewer. The primary drawback of this method is that it is time intensive. Other methods have been developed. Staining methods are primarily used to determine yeast viability, including the industry standard methylene blue test. For the homebrewer, these tests just aren't an option.
So what can the homebrewer do to test for yeast health? You can check viability by inoculating a small starter and checking the lag time. Although this is not always a good measure of viability, it should suffice for the homebrewer.
The smack pack from Wyeast gives the homebrewer a measure of the yeast's overall health. You simply smack the package of yeast to break the nutrient inside. The yeast will consume the nutrient and give off CO2 to expand the package. The quickness of this expansion will give an idea of yeast viability. The date on the packages also give an indication of viability.
You can also go to MrMalty.com to use the pitching rate calculator. Jamil has put a viability algorithm in his calculator which will take the age of the yeast into account when determining the proper amount of healthy yeast to pitch (a very cool idea).
The date on a Wyeast package is the production date. The date on a White Labs vial of yeast is the "best by" date and the production date for calculating viability is 4 months prior the "best by" date on the vial (6 months for bacteria and brett). Yeast viability for most of the homebrewers is not a quantitative but qualitative test of yeast performance.
Do what you can to assure your yeast are stored under the optimum conditions. Store your yeast cold, use as quickly as possible, when the yeast are from a previous batch, and you will be storing for a few weeks or more, wash your yeast with distilled water. Supposedly it is not a good idea to store yeast on the trub as it reduces the yeast viability. Again, wash the yeast and discard the trub before storing. Don't re-use the yeast too many times. There are many sources giving many different values for how many times you can re-pitch a yeast slurry. I generally don't re-use yeast more than 3 or 4 times due to the increased possibility of contamination. I'm not too worried about mutations because I don't plan on re-using the yeast that many times. No matter how diligent you are about sanitation, there is always some degree of contamination in every new batch from a re-pitch, so just be sensible and keep the batches to a minimum.
Vitality measurements are way beyond the scope of this article and involve stressing the yeast and then measuring fermentation results. I'm sure you can find technical articles written on the subject online.
Information for this article was adapted in part from the article Yeast Propagation and Maintenance: Principles and Practices by MB Raines-Casselman, Ph.D.