It's amazing what you can learn on the internet, especially when looking for something totally unrelated! :)
Caulobacter crescentus is a really cool little bacterial species with a funky two-phase lifestyle. The "stalked cells" attach themselves to rocks or whatever in the freshwater environments where these guys live. When a stalked cell divides, part of it remains a stalked cell and part splits off into a "swarmer cell". The swarmer cells swim around like more 'normal' bacteria.
Check out some images of these dudes. (Blogger's image uploader is misbehaving so you guys get a link to Google Images. Sigh.)
They're a fascinating organism to study because their cell division is asymmetrical. If you think back to the high-school-biology version of mitosis... well, it seems like a totally symmetrical process, right? There would seem to be no reason for a particular set of molecules to end up in one daughter cell and not the other, because everything's floating freely around in a droplet of water anyway. But in an asymmetric division like this, the two daughter cells have to develop in different ways. The stalked cell has to keep maintaining its stalk, but the swarmer cell has to grow a flagellum and start making the necessary sensory proteins to swim toward yummy-smelling food molecules. And not only that, but there's a correct orientation for this difference and an incorrect one. It would be kind of awkward if the new stalked cell started trying to swim away, and the swarmer cell floated around trying vainly to anchor to something.
So there must be some sophisticated mechanisms at play here. Notably, it's not that the two daughter cells end up with different genes -- after all, the swarmer cell will later settle and put down roots as a stalked cell. What matters is the presence (or absence) of proteins and other molecules that regulate those genes, so the stalked cell can keep making stalk proteins while the swimmer turns those genes off and turns on the ones for making a flagellum.
This asymmetric division isn't just some strange bacterial phenomenon. Every multicellular creature goes through this kind of process as it grows from a single cell (a fertilized egg) to whatever elaborate body it has as an adult. Figuring out the origins of symmetry-breaking in cell division is one of the major problems of developmental biology.
It also has to do with stem cells, by definition. The vast majority of cells in your body are "terminally differentiated" -- that is, they've gone from nondescript round blobs to fully elaborated cells with sophisticated morphology, heavily optimized for doing whatever job it is they need to do. But the 'terminally' part means they stop dividing once they reach maturity. So if you lose some mature cells, you need to get new ones from a renewable pool of immature cells. These are stem cells. The key defining feature of a stem cell is that it can divide asymmetrically. One of its progeny will be a precursor cell, traveling inexorably down the path to neuron-hood or white-blood-cell-hood or whatever. The other will be a new stem cell, all set to keep hanging in the lazy infinite loop of waiting until it's needed again.