In Revenge of the Sith, Obi-Wan picks up Anakin's lightsaber. The two had fought with them earlier, the two blue blades dramatic against one another.
In A New Hope, Obi-Wan gives "your father's lightsaber" to Luke. Not counting those times when it still looks white in the DVD, it generally looks green.
The main exception is when Luke first activates it in Obi-Wan's house on Tatooine. There, it does indeed appear blue, though not so richly blue as Obi-Wan's.
1. Obi-Wan mixed up which lightsaber in the case was which.
2. Obi-Wan was just randomly lying again.
3. Lightsaber colors are variable with tuning. (This would mean that the lightsaber was only briefly blue as it 'warmed up', then went to its de-tuned green. Green lightsabers might de-tune to some other color.)
4. Lightsaber color changes with age. (This would mean that crystals or other components would change over time, so that a blue lightsaber would become green over the years. While an interesting idea (think of Yoda), I don't think it works given Luke's new lightsaber that was green, or Obi-Wan's blue one.)
5. Lightsaber color changes with battery life. (This would mean that after a brief burst of battery power making the saber blue, it went back to the low-power green. But again, we have the issue of normally-green sabers. Perhaps the blue sabers were a newer technology.)
I'm against #2 on general principle. #1 is a possiblity, but a disappointing one that I'm against on aesthetic grounds.
That would seem to leave the technological issues. Pity Bob Brown isn't around to help guide us as to which is correct. Perhaps at some point I'll do some further research to see what can be gathered about the situation. As it stands, though, I'm somewhat fond of #5.