This Knol provides very simple step-by-step instructions on how to "hide" columns related to the content type in a document library. Hidden columns are not displayed (other than in the properties of the document library, not individual items). The most common use I have found for this is to hide the "Title" column in document libraries where this would simply be a duplicate of the file name.
Go into the properties of your document library. For the purposes of this example I'm going to use a Document Library that is used to save SQL Server Reporting Services Datasets;
The column I intend to "remove" is called "Title - HIDDEN" and is shown above (second from top).
Scroll up on the document library properties and look at the section titled "Content Types";
For this specific document library I am looking at there is a single content type. In this case "Report Builder Report". Click on this to edit it;
Scroll down until you get to the "Columns" section;
Click on the "Title" column to edit it;
In the "Column Settings" section you have three options; Required (Must contain information), Optional (May contain information) - usually the default, and Hidden (Will not appear in forms).
NOTE: Now as the column will still, technically, be attached to the list (it just won't be displayed) I find it useful to append "- HIDDEN" to the name of the column so people don't expect to see it and don't go and edit the properties (which, be warned, makes it visible again).
Select "Hidden (Will not appear in forms)" and click "OK".
Go back to your document library and either create a new item or edit the properties of an existing item - the field is no longer available.