Can I use Google Play Services geofences to get location profiles without a service running all the time? Apps like Llama let you use location-related properties (such as Wi-Fi network visibility) to trigger automation actions such as putting the phone on silent, but they do this by running as a background service and polling for Wi-Fi networks or directly for location.

The Google Play Services library contains a geofencing facility, which allows apps to define geofences and to be started in response to (the phone) entering or leaving those geofences.

Since Google Play Services already needs to run and update my location for things like Google Now and Location History to work, I'd like to be able to use this to have it automate things on my phone, without having an extra service in memory all the time and running periodically. Is there a way I can set this up on my phone? Perhaps there's an app like Llama but using Google Play Services geofences instead of Wi-Fi, or a way to configure Tasker so that it only runs when triggered by a geofence I define. (I've never used Tasker.)
The AutoLocation add-on for Tasker allows you to do this. It makes use of Google Play Services Geofences, and is put out by one of the most reputable Tasker add-on designers around.

To set it up once you've installed Tasker and AutoLocation, create the geofences in the AutoLocation app and click start geofence. Then in Tasker you can set profiles to start from an Event. Choose Plugin, then AutoLocation, then Geofence, and set up the condition. Be sure Tasker is enabled (if the app icon in the action bar isn't coloured, long-tap it). Tasker does have a foreground service (always-on notification) by default: you can disable it from Tasker's preferences.

One shortcoming of this technique is that AutoLocation's geofences only create events in Tasker, not contexts, so you can't have settings changes automatically undo themselves when leaving the geofence.