Dropping unnamed constraints

For dropping an individual unnamed default constrain on a column use the following code:

DECLARE @ConstraintName VARCHAR(256)
SET @ConstraintName = (
     SELECT             obj.name
     FROM               sys.columns col 

     LEFT OUTER JOIN    sys.objects obj 
     ON                 obj.object_id = col.default_object_id 
     AND                obj.type = 'F' 

     WHERE              col.object_id = OBJECT_ID('TableName') 
     AND                obj.name IS NOT NULL
     AND                col.name = 'ColunmName'
)   

IF(@ConstraintName IS NOT NULL)
BEGIN
    EXEC ('ALTER TABLE [TableName] DROP CONSTRAINT ['[email protected]+']')
END

If you want to do this for a default column, which is probably more common than the original question and I'm sure a lot of people will land on this from a Google search, then just change the line:

obj.type = 'F'

to

obj.type = 'D'

There is not a built in procedure to accomplish this, but you can build your own using the information in the information_schema views.

Table based example

Create Proc dropFK(@TableName sysname)
as
Begin

Declare @FK sysname
Declare @SQL nvarchar(4000)
Declare crsFK cursor for

select tu.Constraint_Name from 
information_schema.constraint_table_usage TU
LEFT JOIN SYSOBJECTS SO 
ON TU.Constraint_NAME = SO.NAME
where xtype = 'F'
and Table_Name = @TableName
open crsFK
fetch next from crsFK into @FK
While (@@Fetch_Status = 0)
Begin
    Set @SQL = 'Alter table ' + @TableName + ' Drop Constraint ' + @FK
    Print 'Dropping ' + @FK
    exec sp_executesql  @SQL
    fetch next from crsFK into @FK
End
Close crsFK
Deallocate crsFK
End