Best way to store an unordered list? I apologize if this question has (undoubtedly) been asked before, however I've been hearing conflicting advice from colleagues and the internet.  

I have a table of "groups" and each group has a list of members.  My initial implementation plan was to have a table that mapped user IDs to group IDs.  However, a colleague suggested using a different method, where members would be stored in a blob of information related to a "group" entry.  I cannot remember why this was suggested, but he seemed to think it would be more efficient because a member-group mapping table could grow very large, very quickly.

I can't see why it would be a better approach, but I suppose I'm just asking if there is a better alternative to simply having a user ID - group ID map table?

Thanks for your time!
Within a database, what you're describing is a table. Tables do not have order, but the data can be indexed to allow easier maintenance and retrieval. 

You could always store data as a CSV list, XML, or a variety of other methods, but you should also consider what you're going to do with your data, and you're likely to find that a table ticks more boxes than most. If you're concerned about space, then compression strategies will help a lot, without losing the searchability.