Update via Jack Dougherty:
Updated on February 26, 2015: The friendly folks at YouCanBook.Me tell me that the “On Duty” feature (which displays my office hours, as described below) now requires a paid premium-level subscription OR a free non-profit account. Users who log in with an .edu email address automatically qualify for a free non-profit account, or you can request one by visiting their Non-Profit help page. Also, for more up-to–date instructions, see also YouCanBook.Me’s own tutorial on using the “On Duty” (aka “office hours”) feature.
I have used a number of different websites over the years to streamline appointment scheduling with students. Unfortunately, whenever I find something that seems to work (Tungle.me or “Google Appointments”) they end up going out of business.
So, my current implementation involves yet another niche website that I hope will last a bit longer. It also involves a set of instructions which, though lengthy, provide for a very effective synchronization with my Google Calendar.
Here is the service: http://youcanbook.me/
Here are the instructions: http://commons.trincoll.edu/jackdougherty/2012/12/16/youcanbookme/
And here is my current implementation (this is active so don’t set-up an appointment with me unless you need to!): http://michaelbnelson.youcanbook.me/