Try it for some routes you are familiar with:

http://www.openstreetmap.org/directions?engine=osrm_car&rout...

It varies around the world, for the US (which I'm more familiar with) intercity is pretty solid, last mile stuff you might be missing a street.

Searching for a specific address can be an issue, but road data is pretty good.

The address data is quite partial, which makes searching for locations more difficult.

The road data is very good to excellent in most of the developed/Western world, particularly in Europe.

The footpath data is really the only available of online global maps, and is often excellent (down to details of surface quality).

The POI data is very good in continental Western Europe (down to trees, benches, water fountains etc), and then otherwise will vary depending on the city, or the country.

I've used OSMAnd on my phone and found it to be comparable to or better than a standalone Garmin unit, but nowhere as good as Google Maps. That's doing the route calculations on the phone itself using pre-downloaded data, and I'm not sure how much detail gets stripped in the packaging process. You can't search for a particular house number, for example. In some states and on some highways it'll tell you which lane you need to be in for the right exit ramp, but that level of detail seems to be pretty spotty.

Depends on the application. The developers that made Valhalla (Mapzen) recently hired my doctoral program office mate Indy Hurt to answer some aspects of that question. She's on Twitter at @indymapper. Elsewhere in academia, Muki Haklay has been studying the problem -- here's a link to one of his original papers that can provide a seed to find his more recent work: http://www.ucl.ac.uk/~ucfamha/OSM%20data%20analysis%20070808...

There are also numerous dev gatherings that examine OSM applications and data quality. One starts in a few days: http://stateofthemap.us/program/ You might check out the program and see if your application area is addressed.

Summary: OSM data offers the best free geospatial vector data available. It is a good starting point. For serious commercial applications, however, the data are rarely ready "out of the box". You will almost certainly need to improve/transform/annotate the data for your own purposes. Keep in mind that consequential improvements are expected to be submitted back to the OSM project.