General:
* Cord
* Twine
* Line
* Cable
* String
* Filament
* Strand
More specific:
* For hanging things: Clothesline, clothes rope, laundry line
* For tying things: Binding, tether, lashing, tie
* For climbing: Climbing rope, belay rope
* For sailing: Halyard, sheet, line
* For fishing: Fishing line, leader
Other options:
* Thick cord: Braided cord, hawser, cable, whipcord
* Rough cord: Twine, hemp, jute, sisal
* Thin cord: Thread, yarn, filament
The best word to use depends on the specific context and what you are trying to describe.