I just spent a few hours to find out how to work with Access databases from R. The solution was a simple 32bit / 64bit mix-up:

First, I used this pdf to install the ODBC drivers. What was new here as opposed to all other sources I found while googling, is that he added the source in the tab “System DSN” instead of “User DSN”. Here, I downloaded the Access 2010 drivers, but the R command odbcConnectAccess2007() worked fine as well.

The second secret was to use the 32bit version of R. This was mentioned nowhere, and I only stumbled on this solution by accident.