If I buy a tube of liquid yeast from my local homebrew store and throw it in the fridge, how long before it's no good? How 'bout dry yeast?
Your liquid yeast should have an expiration date. Most dry yeasts will as well. This means that the yeast within is only going to be reproducing and active for that long. Typically 3 months after shipped.
When yeast run out of food or are under other forms of stress, they will enter a sporulation phase. During this process, the yeast will transfer vital cell parts and DNA in to a spore. Spores can live very long periods of time. I'm not sure how long yeast spore live but other Fungi spores have been known to live for upwards of 250 million years.
You should be able to make a yeast starter and bring yeast spores back to an active state within a couple days if feed and stored at ideal reproductive temperatures regardless of how long you've had them.
Theoretically yeast can be stored indefinitely. Yeast goes into a state of dormancy once all of it's food is gone. However yeast can die if not stored properly. If you plan on keeping a yeast culture for more than six weeks, it's a hood idea to make a starter prior to pitching. You do this to ensure viability of the culture, and also to help "wake up" the yeast.
Here's a link to a BYO Magazine article about yeast storage and reusing as per request.