OpenStreetMap is mainly about gathering and distributing geographic data for free (e.a. using a CC-by-SA license). So you can get our data or even pre-rendered tiles, the rest is up to you. Everything you can think of using geographic data should be possible if your programming skills and fantasy allow it. There are already a lot of applications that use the OSM data which might be suitable for you as well.
We have the OpenLayers javascript client (OS GoogleMaps counterpart), Google earth alternative Kosmos, navigation software Gosmore, Navit, Traveling Salesman etc. It’s just too much to list here. Browse the osm wiki and you might find what you need.