Behind the Scenes
1. Lightsaber props were made from random junk.
2. Saber props used to actually "glow."
1. Lightsabers aren't actually made of light
This "fact" is possibly not canon any longer due to the recent continuity changes, but it's been pretty well-established in the Expanded Universe thus far that lightsaber blades aren't "lasers;" they're tightly-wound loops of coiled plasma (the stuff stars are made out of) held in place by a magnetic field. So really, they're plasma chainsaws.
2. Lightsaber blades are opaque
Saber blades apparently block energy, like force fields and blaster bolts. So it makes sense that they'd also block light. This is a screencap from The Clone Wars season 1, "Defenders of Peace:"
Apparently whatever light is shining on Ahsoka is actually brighter than her lightsaber. As someone once put it, "it's like shining a flashlight on a glow stick." It'll still cast a shadow.
3. Lightsabers aren't that bright
For some bizarre reason, lightsabers rarely cast light on other objects near them. Now, in the OT era, this makes sense, as special effects technology wouldn't necessarily allow for that. Or perhaps the science of saber blades is, in fact, much more complicated than we might think, and they really don't cast light on other objects somehow. But then we have scenes like this one from Attack of the Clones:
Clearly, lightsabers actually do illuminate their environment, just to a minor degree. So perhaps they're just not very bright? Maybe the white core of a saber is just an optical illusion of sorts, not actually something bright enough to be white. But The Phantom Menace seems to contradict that.
Here we can see a close-up of Obi-Wan's blade, and (in a brilliant VFX move) it seems that the saber blade is behaving exactly as a white-bright light source does when a camera focuses close to it. In order to counteract the brightness of the blade, the overall exposure is turned down, causing the normally-white blade to appear solid blue. This is proof, of sorts, that lightsaber blades are, in fact, colored blades so bright that they appear white at the center. And they are REALLY bright...
Luke holds his saber up against the sky on Tatooine and it still appears white at the core. So if that's a real representation of the light level of a blade, that means it's brighter than the sky itself, possibly as bright as the sun. And yet it still doesn't actually cast light on other objects.
So yeah. The light levels of a saber blade don't make any sense. The only potential way to justify it is to say that the "camera" is picking up the lightsaber blade the same way cameras often pick up real-world replica lightsabers. Here's an old picture of me holding my Master Replicas Luke FX saber:
Spoilers: it's not actually that bright. At best, it's a solid light blue, but never white like that. The camera overadjusts for the low light and makes it look brighter. Of course, that wouldn't explain why lightsabers in the blinding twin-sun light of Tatooine look white, but oh well.
It seems like for the time being, this is one in-universe mystery that will go unsolved.
4. Sabers move funny
It's a common misconception among geeks that since lightsaber blades are "made of energy," they're weightless, thus when you swing a lightsaber, you're essentially only swinging the handle. That's only partially true, and a lot more complicated.
While plasma is essentially weightless, this doesn't mean that wielding a lightsaber is the same as holding the hilt. George Lucas himself was insistent during the filming of the original Star Wars that lightsabers were supposed to be incredibly heavy due to the incredible amount of energy coursing through them. However, as the OT films progressed and fights became faster, this idea was somewhat dropped. The "official" EU explanation for sabers having weight has been that the magnetic field created by a saber blade causes it to drag through space, essentially simulating mass where there is none.
Now, to be technical, there is a difference between "having mass" and "being heavy." Lightsaber blades do seem to have the inertial effect of mass, as Jedi seem to have to "work with" their blades as any swordsman would. Additionally, lightsabers do have some force of impact on things they hit. Battle droids not only are sliced in half by lightsaber blades, but also buckle under the force of the hit. When Yoda throws his lightsaber at a clone trooper in Revenge of the Sith, the saber "sticks" in the trooper's torso, like a thrown sword or knife.
However, saber wielders don't seem to react to their blades being ignited whatsoever. There's no kickback from the ignition, no sudden weight seems to be applied, no-nothing. It just flicks on as if it were always there, although once it's on, the "simulated mass" inertial effect seems to apply. So the blade itself isn't necessarily "heavy;" it just behaves like a sword when it's swung.
Random interesting note: In the Clone Wars season 1 episode, "Hostage Crisis," Padmé holds Anakin's lightsaber hilt and notes that it's heavy. This might be a reference to the behind-the-scenes "weight" aspect, although realistically speaking, the hilt would actually need some weight in order to provide adequate balance for the "mass" of the blade. Otherwise it'd handle like a baseball bat.
Of course, the "real" reason lightsabers seem to have mass is because the actual props used by the actors do, in fact, have mass, and there's no way to film around that and have it look real. But then again, lightsabers are intended to behave like swords anyway. Lucas himself was insistent upon that fact. So in the end, lightsabers are a bizarre intersection of myth, wonky science fiction, and real sword physics.