Yes, I imagine synthetic ropes would last a lot longer. I won't say that I'm older than synthetic ropes--I think whatever was lying around got used for my tire swing. Hemp, most likely. Just something for someone new to rope swings to think about!
Also, one of the best toys I had at my grandmother's house was a wagon. I got the standard metal Radio Flyer when I was three or four, that was rusted out by the time I was about 6 (because kids will never put them up!). My grandfather build a wooden box, painted it red, coated the heck out of it with sealant, and mounted the old wagon's wheels and handle to it. That was 22 some-odd years ago and that wagon still exists (never even been repainted, although I got better about putting it up on the porch); my step-sister is growing up with it now. Even my grandmother has used it from time to time to haul her gardening tools around the yard.
And can anything top a large box???