Well, as they often say in science: Nothing is impossible.
We just can't do it yet.

However a lightsaber would have to have some kind of laser beam, which would have an end tip, which no laser can do at the moment. A light-beam goes on as long as the light isn't distorted enough, which would result in a lightsaber with near-limitless range (or at least much longer than a standard lightsaber).

Also, it is very unlikely that a lightsaber would be constructable that has the destructive cutting and melting power of the lightsaber, yet would be able to resist other lightsabers, like in the swordfights in the Star Wars movies.

Next to these practical hurdles, would a lightsaber really be the most useful weapon? If possible to construct, why not create a laser gun, and have the additional range?

In our historic weaponry development, swords were created before guns because they were easier to create. With laser weaponry, the opposite is true: A laser gun is easier to create, and much more versatile and powerful than a lightsaber, despite what the Star Wars movies try to make you believe. Remember you need the force to be able to deflect laser gunfire, not just a lightsaber!

All in all, maybe someday a lightsaber might be possible, but there are some serious hurdles to take before it will happen. Plus, its actual usability would be strictly limited, as better weapons would be created much earlier.

i recall reading someplace that it is a beam of energy in an elipse. remember graphing calculators, pre-calc? That's how you can control the length. It's not a laser though. Lasers can't even be seen, unless you cross it's path.

As far as practical usage of a lightsaber, (as if one were needed) it could have some industrial usage. Being able to cut metal like that would be pretty useful. Better than a blow torch or an arc welder.

here's some more info on a light saber from people smarter, or dorkier, than myself.