How do I rename a column in a database table using SQL?

Specifically for SQL Server, use sp_rename

USE AdventureWorks;
GO
EXEC sp_rename 'Sales.SalesTerritory.TerritoryID', 'TerrID', 'COLUMN';
GO

On PostgreSQL (and many other RDBMS), you can do it with regular ALTER TABLE statement:

=> SELECT * FROM Test1;
 id | foo | bar 
----+-----+-----
  2 |   1 |   2

=> ALTER TABLE Test1 RENAME COLUMN foo TO baz;
ALTER TABLE

=> SELECT * FROM Test1;
 id | baz | bar 
----+-----+-----
  2 |   1 |   2