Is it appropriate to ask a professor via e-mail for a letter of recommendation? I have been out of school since May now, and I am considering applying for graduate school. I currently live nowhere near the university I attended. 

Would it be appropriate for me to ask for a letter of recommendation via e-mail? If not, what would be the best option?

[Suggestions as to how I should approach such a communication would be appreciated as well.]
In-person requests are always the best route, because you can gauge willingness and eagerness to write the letters much more directly than via telephone or email.

However, if you can't be there, because you've moved away, then it is of course appropriate to ask for letters by email. Whether or not the professor will grant the request or not is of course a question. However, I would mention that you've moved (and where you currently are) as part of your request, so that the professor knows why you're not able to come in for a meeting if asked.