Unity does not offer such functionality. But Mono does, check out System.Data and especially check out what is present out of the box in Mono 1.2.5 and what you need to drop in (the corresponding dynamic libraries for the database system is required for sure). This all assumes you are using a standalone distribution. Web Distributions can't use non .NET assemblies (and a db access wouldn't be a good idea there anyway as the webplayer is executed locally not on the server, thus making your db vulnerable due to the remote access)
Joining, since it's a vital topic especially for a Web Player deployment. It is possible to run a JS code on the page from the Web Player, so it would be possible to establish db connection.
That will not work. Unity as JS run on the client machine not on the server and you would want a lot but definitely no db connection from the enduser to your db. What you optimally would use is WWW and WWWForm and request the informations from a php / asp / irev / cgi handling backend.