There are 2 ways to remove products that you no longer want in your store. The first, 'Deleting', leaves the product in the database and accessible through Product Manager, but marked as Deleted so it does not appear to customers, and is easy for admins to distinguish from other products. This option can be undone by following the same steps that were taken to delete the product initially (see below), as the 'Delete' link/button will change to say 'Undelete'. The second option, 'Nuking', removes the product from the database entirely, so it will not appear or be accessible anywhere on the site. This is permanent, so only use this option if you are sure you are done with that product.
There are 2 places in the admin site that a product can be Deleted or Nuked:
1 - Go to Products -> Manage Products in the admin site.
2 - Find the product that you want to remove in the grid, and click the Delete or Nuke link on the right hand side.
OR:
1 - Go to Products -> Manage Products in the admin site.
2 - Navigate to the entity containing the product you wish to remove, and click the name of the desired entity in the grid control to open that entity's management page.
3 - Click on the 'Products' tab on the right hand side of the window that opens.
4 - All of the products contained within that entity will be displayed on the right, with a Delete and Nuke button for each. Simply click the desired button next to the product you wish to remove.