How do I duplicate an image in Lightroom 3? I wish to make a version of an image that looks different from the original.
In the Library module, right-click on an image and choose "Create Virtual Copy". This allows two copies of the image to be processed independently (for example, one could be black & white and one could be color).
Because Lightroom does nondestructive editing, you'll still only have one source file on disk (RAW, JPG, etc) but the editing changes will exist in Lightroom. Of course you can always choose to export the "finished" versions of the images.
Besides creating a virtual copy, if your special effects to the images fall in the same workflow, then you can just do Right Click>Create Snapshot at appropriate points in the History palette in the Develop module.
This episode from tv.Adobe explains the use of snapshot vs. virtual copies.