BigTree's BigTreeGeocoding class and the Geocoding field type both rely on the service selected in the Geocoding section of the Developer area. Two services are free to use and do not require a sign-up but are limited. Three services require an API key.
Geocoding Services Without Signup
Google
The default geocoding service is provided by Google Maps and is governed by the Google Maps APIs Terms of Service. In general, this is for low usage scenarios. Excessive use of the Google Maps geocoding API can result in a temporary IP ban from the API.
Yahoo
Yahoo's Placefinder API provides an alternative to Google and is exclusively for non-commercial use. Read the terms of service here.
Geocoding Services Requiring API Keys
Bing
Microsoft provides a geocoding API through their Bing Maps API. It requires an API key that can be obtained here.
MapQuest
MapQuest provides a geocoding API that requires API keys that can be obtained here.
Yahoo BOSS
If you need to geocode a large number of addresses, Yahoo BOSS is your best bet. It is a commercial paid API that you are charged per-geocode for. BigTree caches duplicate queries so you will only be charged by Yahoo for new queries.