Baby_Hitler said:

I'm thinking about keeping a mother culture, and expanding it so that I only have to buy one packet of yeast per type for a very long time.

How would I go about doing that?

How far do you think I could stretch a packet made for a five gallon batch? 

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personally I like the liquid culture yeasts better than the dry. because the yeast have been more fresh than dry packages. http://www.wyeastlab.com/ is a great resource. that's all I use anymore for my homebrews. you want a strain you can brew lots of different beers with. #1056 is a brewery standard.

I use to make "starters" by mixing up some DME for 2-3 12 or 16 oz bottles. about 1.040 Original Gravity. let cool(80f) then "pitch" the yeast into that. let ferment 'till full krotzen (8-12 hr) then pitch into whatever beer I've been making.  oh, put an air lock on the bottle not a cap...messy.
you could always keep the starter in the frig for a few weeks, then use that culture to make more starters.
making new starters I've done that up to 6 generations with out trouble.

the problem when you keep reusing the spent yeast at the bottom is, your pulling in old, dead yeast. and that makes for funny tasting beer.

also, another trick is to brew two batches back to back.
when you rack your beer from the primary fermenter to the secondary, have another batch ready made that day and just use the yeast from the first brew.  but the beers should be similar. not an IPA over a Stout. that would be funny.  I've done that alot with out problems. I think by the third batch  the yeast would need to be washed.

there are ways to "wash" the yeast after a few generations using mild bleach solution and water. basicaly removing the old spent yeast and killing any bacteria.
never did that, but read it sometime ago.

get charlie papazian's book.
hope all my rambling helps somewhat.

Baby_Hitler said:

Some beermakers bottle their beers with a different yeast that what it is brewed with, partly just to hinder yeast piracy.

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