Split function equivalent in T-SQL?

Here is somewhat old-fashioned solution:

/*
    Splits string into parts delimitered with specified character.
*/
CREATE FUNCTION [dbo].[SDF_SplitString]
(
    @sString nvarchar(2048),
    @cDelimiter nchar(1)
)
RETURNS @tParts TABLE ( part nvarchar(2048) )
AS
BEGIN
    if @sString is null return
    declare @iStart int,
            @iPos int
    if substring( @sString, 1, 1 ) = @cDelimiter 
    begin
        set @iStart = 2
        insert into @tParts
        values( null )
    end
    else 
        set @iStart = 1
    while 1=1
    begin
        set @iPos = charindex( @cDelimiter, @sString, @iStart )
        if @iPos = 0
            set @iPos = len( @sString )+1
        if @iPos - @iStart > 0          
            insert into @tParts
            values  ( substring( @sString, @iStart, @iPos-@iStart ))
        else
            insert into @tParts
            values( null )
        set @iStart = @iPos+1
        if @iStart > len( @sString ) 
            break
    end
    RETURN

END

In SQL Server 2008 you can achieve the same with .NET code. Maybe it would work faster, but definitely this approach is easier to manage.

Try this

DECLARE @xml xml, @str varchar(100), @delimiter varchar(10)
SET @str = '1,2,3,4,5,6,7,8,9,10,11,12,13,14,15'
SET @delimiter = ','
SET @xml = cast(('<X>'+replace(@str, @delimiter, '</X><X>')+'</X>') as xml)
SELECT C.value('.', 'varchar(10)') as value FROM @xml.nodes('X') as X(C)

OR

DECLARE @str varchar(100), @delimiter varchar(10)
SET @str = '1,2,3,4,5,6,7,8,9,10,11,12,13,14,15'
SET @delimiter = ','
;WITH cte AS
(
    SELECT 0 a, 1 b
    UNION ALL
    SELECT b, CHARINDEX(@delimiter, @str, b) + LEN(@delimiter)
    FROM CTE
    WHERE b > a
)
SELECT SUBSTRING(@str, a,
CASE WHEN b > LEN(@delimiter) 
    THEN b - a - LEN(@delimiter) 
    ELSE LEN(@str) - a + 1 END) value      
FROM cte WHERE a > 0

Many more ways of doing the same is here How to split comma delimited string?

You've tagged this SQL Server 2008 but future visitors to this question (using SQL Server 2016+) will likely want to know about STRING_SPLIT.

With this new builtin function you can now just use

SELECT TRY_CAST(value AS INT)
FROM   STRING_SPLIT ('1,2,3,4,5,6,7,8,9,10,11,12,13,14,15', ',') 

Some restrictions of this function and some promising results of performance testing are in this blog post by Aaron Bertrand.