A friend of mine runs opencage, which is a geocoder based on open streetmaps and a few other data sets. They got a lot more business when Google raised their prices a while back. Anyway, go give them some love if you need a geocoder because they are an awesome small company with a great service. Their freemium layer is also pretty generous.
Nominatim is the defactor open streetmaps geocoder but its weakness is that it relies on only that; so it is only as good as OSM is.
Geocoding is a surprisingly hard problem to solve with and without open data. Picking apart text strings into unambiguous addresses is just super hard with all the conventions for this around the world. One area open streetmaps is still inconsistent is house numbers and postal codes. Getting solid open data for that is just hard in some places.
Nominatim is the defactor open streetmaps geocoder but its weakness is that it relies on only that; so it is only as good as OSM is.
Geocoding is a surprisingly hard problem to solve with and without open data. Picking apart text strings into unambiguous addresses is just super hard with all the conventions for this around the world. One area open streetmaps is still inconsistent is house numbers and postal codes. Getting solid open data for that is just hard in some places.