I haven't had a clothesline since I lived at my parents' house but I love the smell and feel. On occasion, I have let the sheets dry in the sun on a makeshift line, but normally they just get tossed in the dryer; but it's not the same thing. Not only do the sheets smell great, but you also save energy and money (check out Project Laundry List). It's also healthier because you spend time outside.
As a side note, my husband and his sister wrote a song when they were kids, "on the clothesline" -- a real catchy tune.