For Star Wars fans, what do the different colors of beams in light sabers signify?

The color of lightsaber blades are determined by the type of crystals used in its construction. There are 4 colors featured in the films.

RED

These are wielded by the Sith (bad guys) that have constructed their own lightsabers. Darth Maul (Episode 1) and Darth Sideous (Senator/Chancelor/Emperor Palpatine) have always had red blades. Count Dooku (Darth Tyranus) was a Jedi and used to wield a blue or green blade (never revealed exactly which), but when he became a Sith he made a new lightsaber with a red blade. Anakin Skywalker falls to the Dark Side and becomes Darth Vader in Episode 3, but still wields a blue blade until he is defeated by Obiwan Kenobi on Mustafar, after he gains his new body he builds a new lightsaber with a red blade.

BLUE or GREEN

These are the common blade colors wielded by the Jedi Order. Colors are not assigned based on status (like Padawan Learners, Jedi Knights, or Jedi Masters.) as suggested by a previous answer posted above. In Attack of the Clones (Episode 2) there is a scene where Yoda is teaching a group of Padawan children and there are Blue and Green blades used, not all are blue. Nearly all of the members on the Jedi Counsel are Jedi Masters and they don't all wield green blades.

PURPLE

Only one character wields a purple blade in the films, its Jedi Master Mace Windu, he's a "good guy". The actor that plays him (Samual L. Jackson) requested it as a special favor from George Lucas, one of Jackson's favorite colors is purple.

Many other colors are mentioned in the "Expanded Universe" of Star Wars comics, novels and video games.

YELLOW

The Jedi Knight Bastila Shan from the Kights of the Old Republic video game wields a dual-blade lightsaber (like Darth Maul's) with yellow blades. [The first Luke Skywalker toy by Kenner also had a yellow blade instead of a blue one.]

MULTI-COLORED

The Young Jedi Knights series of novels introduced a more complex design of lightsaber that pulses with two different colors like Orange & Silver, Yellow & Blue, etc.

This is what I've heard from a former boss of mine who's an uber-star wars fan. The light blue are for padawans and jedi knights while the green are for jedi masters. As someone mentioned before, the red are for Sith. The purple means nothing. Samuel L. Jackson had the purple sabre moved into his contract because he wanted to stand out in the fight scenes. But I do think Mace Windu was a jedi master though, if he was on the council.

Oh, and the only reason why Obi-Wan had a light blue one in episode 3 was to keep things consistent going into episode 4; Lucas didn't even have the colours of sabres scheme set up and it was technically easier to create a light blue sabre.

each and every Jedi makes his personal lightsaber as area of there practise the Aldean crystals used, ascertain what colour the blade is. Sith lightsabers are continuously pink because the Sith use man made crystals. in spite of the undeniable fact that in Episodes IV, V, VI all the blades are blue and pink because after the Empire took over administration the grant of diverse crystals grew to develop into very not undemanding to discover and blue is merely the most uncomplicated crystal.

it depends on the person. mace windu is the only jedi to have a purple lightsaber (for a reason that i have forgotten, sorry) however, green, blue, and sometimes white are more common among the ranks of the jedi. as an avid fan knows, lightaber color is depending on the crystal powering it. :P

according to the various novels the color of the lightsaber depends on the gems used in it's construction. so that's why there's yellow, white, green, blue etc.

the reason that mace's was purple is because samuel l. jackson requested it.

Not much, though red is always used by the Sith (evil guys).

It's just there to make it pretty.