Note: Logisim's clipboard is maintained separately from the clipboard for the overall system; as a result, cut/copy/paste will not work across different applications, even including other running copies of Logisim. If, however, you have multiple projects open under the same Logisim process, then you should be able to cut/copy/paste between them.
When you paste components, they will not immediately be dropped; instead, they will be drawn in light gray. They will not actually be ``dropped'' into the circuit until you either move the selection or change the selection so that the components are no longer in it.
The reason for this odd behavior is this: To be consistent with its other behavior, Logisim must immediately merge any wires as soon as they are dropped into a circuit; this merging process changes existing wires in the circuit. When you paste wires from the clipboard, however, you may to place them in a different location, and the changing inherent in the merging process would be against your wishes.
Next: The Project menu.