How complete is OpenStreetMap for US?

Completeness is a relative measurement - you need a reference source to gauge completeness against, as others have indicated. Also, to measure completeness you would need to have a clear idea of which feature types you want to measure completeness for.

Existing efforts to measure completeness in other geographic regions have mostly focused on roads, quite possibly because reference data is most readily available as a reference data set. A notable example is the OSM vs. Meridian data set comparison for the UK done by Muki Haklay and his group. I'm pretty sure an OpenStreetMap vs. TeleAtlas comparison was done for Germany but I can't find it now. Also, Steve Chilton made this comparison of OpenStreetMap and Google - but you'd have to ask him how that was done.

Another approach of measuring completeness - one that I've seen taken in Germany quite a lot, see here for an example - focuses on street names. Local governments usually keep a record of street names in their jurisdiction, and this data can sometimes be easily obtained. You can then proceed to derive a street names list for the same area from OpenStreetMap data and derive a completeness measurement from that. A quick Google search turned up a few US counties that have street names lists readily available on the web.

The data in Open Street Map for the US seems to have originated from data imported from the Tiger Database created by the US Census Bureau. Therefore one could say they are as complete as the US Census Bureau's data, and probably even more so since hundreds of volunteers have been working to update it.

Having said that, one of the prime rules of cartography is "A map is outdated before it is published."

The simple fact is that there are always roads being built, closed, moved, etc. They are a dynamic system. A map is simply a static snapshot of how the roads were* at a given point in time.

[begin platform mode]
The beauty of the Open Street Map project is that instead of waiting for a commercial map maker to (a) find a change, (b) update their data, and (c) get around to publishing new maps; you can make the updates yourself, and they become immediately available for everyone. Better still: instead of having paying the map maker for the new revision, you get it for free!
[end platform mode]

You really have to realize that completeness of any map is a self-contradiction. Completeness, like accuracy, are concepts that are easy to think about but impossible to apply. A point where theory and practice diverge. Victor Borges and Lewis Carrol both have provided great literary commentary on this subject (see http://en.wikipedia.org/wiki/On_Exactitude_in_Science).

Martin (mvexel) has provided links to the leading edge concepts in estimating completeness in user generated databases, like OpenStreetMap. But what he left off was an important aspect of the design of OpenStreetMap. Like Martin, I am an researcher who studies map data quality, especially in systems like OpenStreetMap that incorporate user data contributions. I have had a few opportunities to ask Steve Coast why OSM does not try to quantify data quality. In more traditional databases, like TIGER or the NHD from USGS, there are metadata summaries that provide the map user with an idea of how good the data are. OSM doesn't even begin to do that. Steve's answer, in a nutshell is that if OSM did provide an statement of data quality, it might inhibit people from trying to improve the data. The goal of OSM is to have people with direct knowledge of a geographic area to edit the map. If you see something wrong, you fix it. If someone changes it back, you can see who made the change. Hopefully, that person will be a neighbor (someone else who shares direct knowledge of the geographic area). You will be able to, together, decide on the best representation for that geographic phenomenon.

This idea of managing data quality is not entirely new. Worboys and Duckham (GIS: A Computing Perspective, 2004, p 338-339, http://books.google.com/books?id=x4e2IVV0u9gC&pg=PA338&source=gbs_selected_pages&cad=3#v=onepage&q&f=false) actually describe this as one of the three action types for resolving discrepancies in a database.

In a nutshell, to ask "How complete is OpenStreetMap for the US?" is like asking "How accurate are the historical events in the Bible?" Like the Bible (or any religious text), it should be perfectly obvious that the information on a map is allegorical. Just as the allegories in the Bible have a purpose other than the precise documentation of historical events, the allegories in OSM are not really meant to precisely document geographical features.

Jesusishelena, it is reasonably complete, but while the relationship of TIGER data from streets and intersections are mostly right, they placement can be up to 1/2 mile off in rural areas to 500' or more in urban areas.

My suggestion is get out start editing the map, add in stuff (restaurants, hotels, whatever you know) to it. Many hands make quick work, plus YOU ARE AN EXPERT, certainly in your neighborhood.