This is not too common, but usefull to know anyway. While searching for some answers to this question, I came to realize that the SQL default trace should be enough to find this information. If you are trying to find a reasonably recent information, yes it is.
Just open Windows Explorer, go to your server log folder (like “C:\Program Files\Microsoft SQL Server\MSSQL10_50.<INSTANCE_NAME>\MSSQL\Log“) and open up the last log*.trc file. It will open in SQL Profiler, there you should search for the string “– DB” on the ObjectType column for the events of type “Object:Deleted”. In the DatabaseName column you will find exactly that, and in the SessionLoginName you will have, well, the login of the user who deleted the database.
Pretty easy if your server is not too busy. If it is, you will need to set some form of DDL audit or something. I will investigate on this later.
Some links that can be usefull on this subject:
http://www.sqlservercentral.com/Forums/Topic989304-391-2.aspx (this one has a nice script, but is broken by SQL2008 R2 due to an unexpected “_” character).