Navnelaboratoriet is build by Finn Jordal, and he has written excellent explanations of this mash-up in Danish (links further down).

The mash-ups is based on 2 data sources:
A list of viable names, as published by the Danish Ministry of Justice, which publishes in html and csv.
Statistic info on the usage of names in Denmark, which is scraped from the Statistics Office website.

Finn Jordal combines this into a RESTful interface/API.

Full description of the mash-up in Danish.

It allows you to search for names, and see how many other people over the years have gotten this name, its rank in the list of most popular names, and the occurrence of combinations of first and last name. This you can do on the website of Navnelaboratiet (which also includes links to Wikipedia explanations of the meaning of a name), or by using the API (full API description here) which returns data in XML, JSON and JSONP.

Example output from the website:

A name and its occurrence over time.

With as Finn says, 80 lines of HTML, 79 lines of CSS and 169 lines of Javascript, the mash-up was ready.

Contact: Finn Jordal, http://oiorest.dk, @oiorest

Related: a map of name occurrences in Denmark