Deadlock error isn't returning the deadlock SQL

The data you need is recorded in the default extended events trace.

DECLARE @xml XML

SELECT @xml = target_data
FROM   sys.dm_xe_session_targets
       JOIN sys.dm_xe_sessions
         ON event_session_address = address
WHERE  name = 'system_health'
       AND target_name = 'ring_buffer'

SELECT   
             XEventData.XEvent.query('(data/value/deadlock)[1]')  AS DeadlockGraph,
             CAST(XEventData.XEvent.value('(data/value)[1]', 'varchar(max)') AS XML) AS DeadlockGraph,
              XEventData.XEvent.value('(./@timestamp)[1]', 'DATETIME2') AS [DateTime]
FROM   (SELECT @xml AS TargetData) AS Data
       CROSS APPLY 
       TargetData.nodes ('RingBufferTarget/event[@name="xml_deadlock_report"]') AS XEventData (XEvent) 
ORDER BY [DateTime] DESC

Though it won't be there any more if you have restarted the service -e.g. to apply a trace flag or if the buffer has cycled in the meantime.

You can set up your own extended events trace that stores the deadlock graph to a file target for persistent non volatile storage. Example Code here. I personally find the deadlock graph XML more friendly than the trace flag output.

Edit

1. @MartinC points out in the comments that on instances of SQL Server that don't have all the updates there might be a problem with it generating invalid XML. The fix for that is to do some search and replace and use CAST(REPLACE(REPLACE(XEventData.XEvent.value('(data/value)[1]', 'varchar(max)'), '<victim-list>', '<deadlock><victim-list>'), '<process-list>', '</victim-list><process-list>') AS XML) AS DeadlockGraph in the SELECT list as described here.
2. Wayne Sheffield has posted a useful script to shred the deadlock graph XML into tabular format here.

The accepted answer did not work for me consistently. The ring buffer apparently is known to drop events in certain circumstances..

ConnectItem

Ring Buffer Issues

The system_health log event files can parsed (from this answer):

with XmlDeadlockReports as
(
  select convert(xml, event_data) as EventData
  from sys.fn_xe_file_target_read_file(N'system_health*.xel', NULL, NULL, NULL)
  where substring(event_data, 1, 50) like '%"xml_deadlock_report"%'  
) 
select EventData.value('(event/@timestamp)[1]', 'datetime2(7)') as TimeStamp,
       EventData.query('event/data/value/deadlock') as XdlFile
  from XmlDeadlockReports
 order by TimeStamp desc

The XdlFile field can be saved to an .xdl file and read into SSMS. Tested in Sql Server 2012.