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new openstreetmap router which is very fast:

OSRM Website on Project-osrm
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@Leberwurscht Brot Yes, I can imagine that bike routing works well.

The problems with OSM data for car routing are:

It has to be converted to other formats to make data access fast enough. Not only from XML to a database, but the way the data is organized, in nodes that can hold nearly everything, ways that can also be rivers (iirc), areas that might be a house, a forest or a city boundary — all that doesn't really make sense for routing (starting with the node as an entity altogether).

That can be done, of course, but the main problem is that there is no safe way to find out whether a street is within a city boundary or not, thus average car speeds might be around 30 km/h or around 80 km/h, which makes a big difference for choosing routes and also for guessing ETAs, of course.

If there is a city boundary defined, one could use insideness testing for that, but it is often an administrative boundary that is far outside the city's actual perimeter. Alternatively, one could read the landuse areas that define industrial or residential use etc.. There are just too many possibilities to really make good guesses. And quite often none of these areas is defined at all, only a single node at the center of the village that shows its name on the map but doesn't hold any information whatsoever (apart from rough size categories) about how large the city actually is.

There is the possibility to set a maxspeed for a way, but it's not widely used.

Same for turning restrictions; they can be set but often aren't, as many OSM contributors focus on map making.

To really get usable car routing, OSM data would have to be combined with a road speeds database (which nobody tried to build yet, afaik), and it would have to be used more widely for routing so that more people add missing routing data.

Pedestrian routing and bike routing should work very well, though.
Funny, I just stumbled on that myself. It's pretty good, though a little rough at some edges. Good thing is, it exports calculated tracks to GPX, which could then be fed to OsmAnd (or several other mobile OSM mappers), so that I'll be able to travel without internet access for a few weeks. This is just great.