Can I assemble an Apple labeled hard drive in another laptop? A lot of hard drives delivered with Macs come with an Apple logo. 

Is it possible to put those drives in other laptops like Asus, Acer, Toshiba etc.?
Those hard drives are OEM-drives build by Seagate, Toshiba or other hard drive manufacturers for Apple.

Usually there should be no problem to put them in other non-Apple laptops if they fit physically.

You won't be able to mount the HFS-volumes on those drives without special file-system drivers like Paragon's HFS+ for Windows in a dual-bay configuration.

There might be rare cases however, where drives with Apple firmware in conjunction with special SATA- or IDE-controllers used in non-Apple laptops might not work reliably. Without knowledge and special hardware it's almost impossible to detect occurring errors (e.g. bit-errors).