Fireflies put on the red light 1 using a chemical called luciferin ("light bearer") and a special enzyme that catalyzes its oxidation, luciferase. Each molecule of luciferin can only be used once -- another word for oxidation is burning. Since it takes energy to produce each luciferin molecule, it's a bit of an expensive way to identify yourself to potential mates, but obviously worthwhile for some. And, of course, many humans find it fascinating and even beautiful: minor molecular subsitutions in the luciferin molecule cause large color changes 2, so a given insect species can luminesce red, yellow-green, or blue, and some do more than one at a time.
Sea creatures also do a lot of luminescing, like the now iconic anglerfish when she wants to attract other deep-sea creatures to eat.
Some make their own luminescence like the firefly, while others recruit bacteria. Overall, bioluminescence occurs naturally in animals, fungi, and protists as well as those ubiquitous prokaryotes 3. Something about the plant lifestyle doesn't seem conducive to it; I'm going to guess that would be the complete dependence of almost all plants on high levels of externally applied light.
Plants aren't without the ability to emit photons, though; they just don't make them non-renewably. Fluorescence occurs when a molecule moves into an excited (higher energy) state upon being hit by a photon, then emits another photon to return to its ground (regular amount of energy) state. The major differences from luminescence are that the fluorescing molecule is often fine afterwards -- they wear out eventually, but they're no one-shot luciferin -- and that you need light to make light. The energy return isn't perfectly efficient for reasons I won't go into 4, so the wavelength of the fluoresced photon is longer than that of the photon that hit the molecule originally. So a blue photon exciting a molecule can cause emission of green or yellow or orange photons, or, importantly for plants, it can pass its excitation to another molecule. This is what chlorophyll does all day: collects light energy and passes it along to other molecules that use the energy to make sugars out of carbon dioxide. Plants use the sugars in mitochondria to run their cells 5, just like us, and also for constructing their cell walls so they can grow.
Ideally, then, chlorophyll shouldn't fluoresce, because it's better for the plant to use that energy once it's caught. It's very easy, though, to puree a bunch of leaves and extract the chlorophyll. Once the molecular arrangements of the chloroplast are disrupted, the chlorophyll has no organized protein chain to give the energy to, and you can see its red fluorescence. Floral organs also often fluoresce beautifully, though I hesitate to claim much adaptive significance for that when the reflected UV patterns likely swamp any daylight fluorescence.
Aequorea victoria, sometimes called Aequorea aequorea (Emily, take note!), is a fascinating animal. It's bioluminescent, breaking down a molecule called aequorin in a similar process to luciferin luminescence, but it's also fluorescent. The aequorin-created light is blue, and the blue photons excite Green Fluorescent Protein (GFP) 6, which puts out green photons. This is a lot of ongoing work to do just to glow in a fancy color!
Aequorea victoria, copyright Sierra Blakely, via Wikimedia Commons.
None of the jellyfish structures in this image are luminescing or fluorescing. That's reflected light.
For the green lights, see the left sidebar of this page.
My big question was, why does Aequorea want to appear green so badly? Making all that light is so metabolically taxing that any biologist's first thought should be sex -- unless there are direct fitness boosts from doing it, nothing costly, risky, and convoluted should be selected for. It's surprising, then, that Aequorea's sex life has nothing to do with meeting in person. Oh, and another small detail? They don't have eyes. The only rationale I've heard that makes sense is that, since Aequorea jellies luminesce when disturbed, the light emission is a way to startle potential predators into backing off. The green wavelengths may thus be more surprising in a predominantly blue-lit environment like the ocean.
For more about Aequorea and its relationships with GFP and the media, check out our own Friday Harbor Labs scientist C.E. Mills' page on the matter.
Next time: why GFP is important for molecular biology. -- KMP
 The organisms are not necessarily happy when luminescing, actually. Sad advice strongly implied at the Firefly FAQ is to traumatize or kill them so they'll glow consistently for longer when taking photographs.
 Yes, some of them glow red, generally South American ones. Mostly I just couldn't resist the "Roxanne" reference.
 Gandelman et al. (1993) Oxyluciferin fluorescence is a model of native bioluminescence in the firefly luciferin—luciferase system. Journal of Photochemistry and Photobiology B: Biology 19(3):187–191.
 Here's one great survey of bioluminescent organisms, with unfortunately messy html that I attribute to an apparent site move.
 Well, if you're that interested. http://en.wikipedia.org/wiki/File:Electronic_Processes_Involving_Light.png
 With oxygen. Yes, really.
 Note the super creative naming for which we scientists are known in this paragraph.