The lightsaber is the weapon of a Jedi, an elegant weapon of a more civilized age. In comparison, blasters are crude, inaccurate and loud affairs. To carry a lightsaber is an example of incredible skill and confidence, dexterity and attunement to the Force. In the hands of a Jedi, a lightsaber is almost unstoppable. It can be used to cut through blast doors or enemies alike. Using the Force, a Jedi can predict and deflect incoming blaster bolts, and reflect them back at the firer.
Although use of the lightsaber is the mark of a Jedi -- the only ones capable of handling the difficult weapon -- it is also used by their sworn enemies, the Sith.
The lightsaber is the most recognized symbol of the Jedi Order. Younglings study with training lightsabers of limited power -- and thus limited danger -- before they are tasked to construct a weapon of their own. To hear a common Jedi teaching, "this weapon is your life." Padawans are expected to closely guard their weapon and never let it fall into untrained hands.
The Sith also wield lightsabers. The Sith Order was an offshoot of the Jedi, so it is only natural that they took the lightsaber with them as their preferred weapon. Sith lightsaber combat tends to be more aggressive, to more naturally channel hateful emotions. Sith lightsabers have red blades.
General Grievous is not a Jedi, though he imagines himself as capable of any Force-imbued warrior. In truth, Grievous cannot touch the Force, and instead relies upon his advanced cyborg anatomy to give him the skill and speed required to wield a lightsaber. Grievous carries lightsabers plucked from the bodies of defeated enemies.
A lightsaber can fetch a pretty price in the underworld market. A pickpocket stole Ahsoka Tano's lightsaber, and a convoluted chain of events led to that lightsaber falling into the hands of a killer. From there, it entered into the possession of thief Cassie Cryar, who led Ahsoka on a winding chase through the city.
Count Dooku is regarded as one of the finest swordsmen in the galaxy. He carries a lightsaber with an elegantly curved handle, a throwback to a more classical age of combat.