Multiple Columns as Primary Key?

I was questioning whether my database design was a good one. This is my first project using SQL (or any database for that matter) and I wondered whether using multiple columns as a primary key was "good design" or, alternatively, if I should just create a dummy column in my tables and use the IDENTITY property (so that they are auto-numbered and guaranteed unique). I guess this is a hotly debated issue. I found quite a few discussions on the web about it--with people arguing adamently in both directions.

Here are a few links.

1. "Primary Key" (Google Groups).
2. "Design: multiple columns for primary key" (Google Groups)
3. "SQL Server Performance Questions & Answers" (in favor of IDENTITY columns)