How to copy paste layers from one QGIS project to another?

just right click the layer and select save as...layer definition file and save... then from another project, click the layer menu and select add from layer definition file... and that's it. ;-)

There is a plugin named Layers menu from project that lets you import layers from other project files incuding the styling.

The only pitfall: Attention : the project must be configured to record absolute paths which is not the default for QGIS. But you can change it in the project properties.