From OpenStreetMap Wiki
Search engine services
These options are available as services you can call:
- Nominatim is deployed on OpenStreetMap servers, and powers the search on the front page as well as offering an API.
- LocationIQ.org runs nominatim with OSM data but on SSDs
- MapQuest also run nominatim with OSM data as part of their open initiative
- YaCy - a P2P open source search engine
- OpenCage hosted by Opencage Data Ltd - searches across OpenStreetMap, geonames, geoplanet among other sources.
- Photon hosted by Komoot.de
- GeoCheck hosted by IdeesLibres.org - searches across Nominatim OSM, Google, Photon OSM, ideeslibres.org BANO, IGN, Etalab BANO
- Osmocoder hosted by 123map.de, able to do batch geocoding, so far for area of Germany, and in German language.
- OSMNames maintained by KlokanTech.com and HSR - provides basic search in place names with autocomplete for demo purposes. The project mainly aims to deliver gazetteer data from OSM.
- Mapzen Search provides the Pelias geocoder as a web service to search across OSM, OpenAddresses, Geonames and Who's on First including a free tier.
Search engine software
These options can be deployed to your own server:
- OSMonto - a
- Pelias is the software behind Mapzen Search providing autocomplete geocoder and reverse geocoding based on various open data sources and Elasticsearch.
- geopulse-geotag by factual.com
- OSM-Gazetteer by Dmitry Kiselev
- Oscar with a tiny description in 
- OSMNames SphinxSearch by KlokanTech.com - easy to deploy with Docker and downloadable data from OSMNames.org
- osmgeoref – a small geocoding engine with low resource requirements
- Twofishes - by Foursquare - A coarse forward & reverse geocoder in scala