Do any database “styles” use discrete files for their tables?

Question

I've been talking to some people at work who believe some versions of a database store their data in discrete tables. That is to say you might open up a folder and see one file for each table in the database then several other supporting files. They do not have a lot of experience with databases but I have only been working with them for a little over a half year so I am not a canonical source of info either.

I've been touting the benefits of SQL Server over Access (and before this, Access over Excel. Great strides have been made :) ). But, other people were of the impression that the/one of the the benefit(s) of using SQL Server over Access was that all the data was not consolidated down into one file. Yet, SQL Server packs everything into a single .mdf file (plus the log file).

My question is, is there an RDBMS which holds it's data in multiple discrete files instead of one master file? And if the answer is yes, why do it one way over the other?

edit

Thank you everyone for you're answers. This has really helped clarify the whole situation.