Getting the minimum of two values in SQL

SQL Server 2012 and 2014 supports IIF(cont,true,false) function. Thus for minimal selection you can use it like

SELECT IIF(first>second, second, first) the_minimal FROM table

While IIF is just a shorthand for writing CASE...WHEN...ELSE, it's easier to write.

Use Case:

   Select Case When @PaidThisMonth < @OwedPast 
               Then @PaidThisMonth Else @OwedPast End PaidForPast

As Inline table valued UDF

CREATE FUNCTION Minimum
(@Param1 Integer, @Param2 Integer)
Returns Table As
Return(Select Case When @Param1 < @Param2 
                   Then @Param1 Else @Param2 End MinValue)

Usage:

Select MinValue as PaidforPast 
From dbo.Minimum(@PaidThisMonth, @OwedPast)

ADDENDUM: This is probably best for when addressing only two possible values, if there are more than two, consider Craig's answer using Values clause.

The solutions using CASE, IIF, and UDF are adequate, but impractical when extending the problem to the general case using more than 2 comparison values. The generalized solution in SQL Server 2008+ utilizes a strange application of the VALUES clause:

SELECT
PaidForPast=(SELECT MIN(x) FROM (VALUES (PaidThisMonth),(OwedPast)) AS value(x))

Credit due to this website: http://sqlblog.com/blogs/jamie_thomson/archive/2012/01/20/use-values-clause-to-get-the-maximum-value-from-some-columns-sql-server-t-sql.aspx