When should I NOT set the Maximum Server Memory option in SQL Server? In SQL Server, I normally set the Maximum Server Memory setting to one of the popular best practices, such as leaving 10% or 4GB, whichever is higher. 

http://www.brentozar.com/archive/2012/11/how-to-set-sql-server-max-memory-for-vmware/

I have a new server with 64GB RAM. Due to licensing constraints, this server must run the SQL Server database engine, SSIS, and SSAS. SSIS ETLs happen overnight, and users hit the actual database mostly during the daytime. In this scenario, would it be best to leave the default setting so that SSIS can take the memory if needed, and then the database engine can take memory when it needs it?
You should always set your max memory away from default and leave some room for OS (see Jonathan's post of how much Memory to leave based on the amount of RAM installed).

Jonathan Kehayias has blogged about : How much memory does my SQL Server actually need?


  reserve 1 GB of RAM for the OS, 1 GB for each 4 GB of RAM installed from 4–16 GB, and then 1 GB for every 8 GB RAM installed above 16 GB RAM.  


You can also refer to my answer here for more details.


  would it be best to leave the default setting


NO, dont leave it as default as problems like OS unresponsiveness, Working Set trimming as well as other applications running on the server will be affected adversely. It will affect your backups as well.

Note that Memory Manager for SQL Server 2012 and up has changed.