If I recall, the color of a blaster bolt (character-scale or starship scale) is determined by the quality of the gas used in it - higher quality gives you green, lower quality gives you red. The Rebellion didn't have access to the highest quality gas, and had to make do with the lower quality ammunition.
(An aside: Yes, gas. That's what they collected at Cloud City - Tibanna gas, essential for the creation of blaster ammunition)
With lightsabers, it's all decided by the color of your focusing crystal. Blue, green, and red are most common, but other colors aren't unknown. Synthetic red crystals are also common among the Sith, who prefer the speed of synthesizing to the quality of those you can discover naturally. Vader and Palpatine both used synthetic crystals in their lightsabers.
Interestingly, if you put enough time and effort into creating a synthetic crystal, it can end up any color - both Luke's lightsaber from ROTJ and Jaina's lightsaber (from the Young Jedi Knights book Lightsabers) are synthetic. Luke is described as spending months on his crystal in Ben's hut on Tatooine, and Jaina spends considerable time and effort on hers.
In the era of the Old Republic, the color of lightsaber a Knight used was a mark of his caste - Guardian, Consular, or Sentinel. This tradition was NOT carried over into the New Republic era, and may have fallen out of use by the time of the Clone Wars - it's never made explicit if such distinctions between Jedi were still made (other than Padawan/Knight/Master).
Lightsaber color has been extensively referenced. Off of the top of my head, look at KOTOR (the original game and sequel, as well as The Old Republic RPG), I, Jedi, the Young Jedi Knights book Lightsabers, and the Jedi Academy Trilogy.
There's also references in the Wookipedia article for Blaster Gas that help explain the different colored bolts.
Edit the second:
All of this is 'Legends' or 'Infinities' now, and may be completely overturned by Episode VII, now that Disney owns Star Wars and has changed Star Wars canon rules. Episode VII may 'reveal' that lightsabers are powered by worms that feed on your midichlorians, and this answer may end up completely wrong as a result. As it stands, it is accurate to the best of my knowledge, using sources which are no longer considered 'trustworthy' with regard to future works.