What is the benefit of using "SET XACT_ABORT ON" in a stored procedure?

SET XACT_ABORT ON instructs SQL Server to rollback the entire transaction and abort the batch when a run-time error occurs. It covers you in cases like a command timeout occurring on the client application rather than within SQL Server itself (which isn't covered by the default XACT_ABORT OFF setting.)

Since a query timeout will leave the transaction open, SET XACT_ABORT ON is recommended in all stored procedures with explicit transactions (unless you have a specific reason to do otherwise) as the consequences of an application performing work on a connection with an open transaction are disastrous.

There's a really great overview on Dan Guzman's Blog,

In my opinion SET XACT_ABORT ON was made obsolete by the addition of BEGIN TRY/BEGIN CATCH in SQL 2k5. Before exception blocks in Transact-SQL it was really difficult to handle errors and unbalanced procedures were all too common (procedures that had a different @@TRANCOUNT at exit compared to entry).

With the addition of Transact-SQL exception handling is much easier to write correct procedures that are guaranteed to properly balance the transactions. For instance I use this template for exception handling and nested transactions:

create procedure [usp_my_procedure_name]
as
begin
    set nocount on;
    declare @trancount int;
    set @trancount = @@trancount;
    begin try
        if @trancount = 0
            begin transaction
        else
            save transaction usp_my_procedure_name;

        -- Do the actual work here

lbexit:
        if @trancount = 0   
            commit;
    end try
    begin catch
        declare @error int, @message varchar(4000), @xstate int;
        select @error = ERROR_NUMBER(), @message = ERROR_MESSAGE(), @xstate = XACT_STATE();
        if @xstate = -1
            rollback;
        if @xstate = 1 and @trancount = 0
            rollback
        if @xstate = 1 and @trancount > 0
            rollback transaction usp_my_procedure_name;

        raiserror ('usp_my_procedure_name: %d: %s', 16, 1, @error, @message) ;
    end catch   
end
go

It allows me to write atomic procedures that rollback only their own work in case of recoverable errors.

One of the main issues Transact-SQL procedures face is data purity: sometimes the parameters received or the data in the tables are just plain wrong, resulting in duplicate key errors, referential constrain errors, check constrain errors and so on and so forth. After all, that's exactly the role of these constrains, if these data purity errors would be impossible and all caught by the business logic, the constrains would be all obsolete (dramatic exaggeration added for effect). If XACT_ABORT is ON then all these errors result in the entire transaction being lost, as opposed to being able to code exception blocks that handle the exception gracefully. A typical example is trying to do an INSERT and reverting to an UPDATE on PK violation.