It is possible to move single parts and assemblies in and out from assemblies by dragging their icons in the scene browser structure. You can also move several of them at once by holding down the SHIFT or CTRL key while dragging and it is also very important that you drop on the target assembly icon (not on something that resides inside/below the target assembly).
1) Select the parts by using the CTRL or the SHIFT key.
2) Hold down the CTRL or the SHIFT key while dragging.
3) Drop on the target assembly icon.
Now all selected parts have been moved to the selected assembly.
See instructions here: http://youtu.be/3_g2CCMUkrI
Another trick is to make a temporary assembly of all the selected parts.
Move the temporary assembly inside another assembly (target assembly).
Disassemble the temporary assembly inside the target assembly.
At the bottom of the target assembly you'll see all the moved parts.