Is there a free, authoritative, trustworthy online database where one can look-up the accreditation of any college or university in the world?
For information about European institutions, the best starting point for such an online search is possibly the ENIC-NARIC network (European Network of National Information Centres on academic recognition and mobility) which lists the national accreditation organisations.
A list of accredited Swiss higher education institutions can be found at the site of the Rectors' Conference of the Swiss Universities CRUS.
A database of accredited study programmes in Germany can be found at the site of the German Accreditation Council.
The Accreditation Organisation of the Netherlands and Flanders NVAO has a similar database of Dutch and Flemish study programmes and institutions.
There is an international database called UNIVCHECK that allows to validate whether a university is accredited or not. It is both a white list and black list.
In US, US news college rankings will give you this information http://colleges.usnews.rankingsandreviews.com/best-colleges
Other databases that you can search are US Department of Education databases http://ope.ed.gov/accreditation/
The Council for Higher Education Association has a Database of Institutions and Programs Accredited by Recognized United States Accrediting Organizations listing schools accredited by US accrediting agencies, but this also includes schools in other countries that are also accredited by these US organizations.
The World Higher Education Database contains around 18,500 institutions from 186 countries. It's maintained by the International Association of Universities, a UNESCO-affiliated NGO.