At 6800 feet (where I live) my resting HR is 55BPM +/- 3 and falling because I've begun to train hard coming off of a really bad injury + surgery. During recovery where I was unable to exercise it drifted up over the months to 62BPM. As I get back into my best condition it'll fall into the low 50s.
At sea level my resting HR will fall by 5-7 beats for a couple weeks and then drift back to stasis over 6ish weeks my body reduces its red blood cell count and all the other acclimatization stuff. I try to avoid this.
I watch it pretty closely because as nabla9's excellent commentary in this subthread highlights, a persistently elevated resting HR is a sign of overtraining, which being a type A obsessive nutjob I am pretty susceptible to. :)
I've also found that an elevated heart rate that can't be explained by overtraining, for me, is indication that I've got an incoming illness that I don't feel yet, usually a sinus infection.
Edit: expanded explanation