On the main products page you can see Copy, Paste and Clone icons. These actions can be performed with more than one product with the help of Products toolbar (1) or products context menu (2).
You can Copy , Paste or Clone products with their attributes altogether.
First you have to copy selected product and go to the category you need. When you're pasting the product, you're creating the new one with the new ID number.
Clone Products option is actually like a combination of copy and paste buttons. It will copy selected product and place it in the same category with the new ID number and the postfix " - clone" at the product's name. This way is easier and faster than copy/paste.