What keeps a lightsaber from going on infinitely?

There is no good physical hypothetical model of a lightsaber. While you could potentially use an electric field to contain plasma in the proper shape, this would (a) take huge amounts of energy to maintain and (b) still probably not exhibit all the sword-like characteristics. Think continuous lightening plus a strong, highly localized field to contain it. Even with magical crystals to resonate (insert appropriate techno-babble) enough energy, the grip would be incredibly hot.

Lightsabers are clearly not lasers, as they are visible, wide, and interact with each other with substantial forces. Sadly, this is one of the "magical" details of Star wars.

According to a lot of the Star Wars Extended Universe info, they actually arc back after a certain distance; it's just not terribly visible in the movies; think of them arcing back in a beam right next to the one emanating for the emitter. (It may help to think of a magnetic field (like the traditional 'Magnetic Bottle') being generated to point the out-flowing energy to somewhere a few feet away, then being 'Capped' there, forcing it to arc back to where it grounds.)

I'm trying to hunt up the article with all of the history on them (they have changed a lot over time), but for the moment, this is probably what you are looking for:

...they developed a method to generate a focused beam of energy that arced circumferentially back to its source, creating a controlled energy circuit and leading to the first portable high-energy blades.

Then,

Once focused by the crystals, the plasma was sent through a series of field energizers and modulation circuitry within the emitter matrix that further focused it, making it into a coherent beam of energy that was projected from the emitter.[25] The blade typically extended about a meter before being arced by the blade containment field back to a negatively charged fissure ringing the emitter, where it was channeled back to the power cell by a superconductor, completing the circuit. Below is a list of the primary parts almost all lightsabers needed to use to function properly:

From: Lightsaber on Wookieepedia

From what I've read, it's best to think of the blade mathematically as an ellipse or ellipsoid with an exceptionally small conjugate diameter, rather than as a straight line. Instead of creating a line of energy that stops at an arbitrary point, it's like creating a BALL of energy that is exceptionally distended in a specific way.

In simpler terms, think of somehow focusing a laser to travel in a very tight circle rather than a straight line, so the light loops around in the shape of a sword blade. Of course, the problem is the "somehow". That's what makes this science fiction. We don't know how to do that right now, but perhaps you can just imagine someone discovering a principle that makes it possible.

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The other way I've heard this explained is as if you are accelerating something like ion particles to near-light speed. Additionally, there is a something like a strong magnet in the handle, with the opposite charge as the ions. So the ions shoot out the emitter, but are attracted to the magnet such that they are decelerated enough to stop about a meter from the handle and drawn back the other way until they are recovered.

I say "something like" ions, because if it were ions and magnets the device would interfere with and be itself interfered with by too many normal materials. But, again, science fiction. You can suspend disbelief by understanding it as a particle type and counter-force we just haven't discovered yet.

Lightsabers have changed little in the thousands of years of their employ by the Jedi Knights. Those who believe the Jedi order began on the ancient world of Ossus point to the abundance of Adegan crystals in the system as proof. These crystals are ideal for the creation of lightsabers, as they focus the energy released from a saber's power cell into the tight, blade-like beam. Early lightsabers did not have self-contained power cells, and were instead connected by a conducting cable to a belt-worn power pack. Once unleashed, the power channels through a positively charged continuous energy lens at the center of the handle. The beam then arcs circumferentially back to a negatively charged high energy flux aperture. A superconductor transfers the power from the flux aperture to the power cell. As a result, a lightsaber only expends power when its blade cuts through something. So efficient is the blade, that it does not radiate heat unless it comes into contact with something.

http://starwars.com/databank/technology/lightsaber/index.html

Some have suggested magnetic fields and plasma:

Shin also recommended adding a degausser sound on top of the other sounds for the weapon since the sound would be reminiscent of a magnetic field.

Design and create a "magnetic bottle." Since the 1950s, the ability to contain plasma and other high-energy particles has been done with electromagnetic containment fields, otherwise known as "bottles." Electrons and other atomic structures have difficulty crossing a magnetic field. By shaping the field, you can direct or contain them. The shape of the field varies, but for the lightsaber effect, the interior of the magnetic bottle will have to be about 3 feet long and 2 inches wide. This requires several focused, high-energy induction coils to be mounted to a heavy iron core disk. The disk also serves as a mount for the hilt.

http://www.ehow.com/how_5056861_make-real-lightsabers.html#ixzz1U8DcZ8IM

One problem with the criticisms from a skeptics point of view (myself) is too many strawman the possibilities. For instance, yes, light would pass though, but the magnetic fields might react with each other. Light might only be present as a visual effect and the actual cutting taking place by some other means. In short, it may be possible to make a ‘light saber’ with some combination of technologies. Some which work together to repel light sabers from each other, other to cut materials, and yet others to create visual effects to guide the use.

Light Sabers are not lasers. They are an energy projection/magnification of the crystal inside of them. It's crystalline structure is barely noticeable due to the intense light that the projection gives off but you can see it at the tip of the sabers. Think of it like a hologram, only one that channels and focuses immense energy into its projection.