So many great ideas and comments here!
Thanks to Brooklyn for inspiring me to wear scarves as toppers in summer.
Thanks to Joy for reminding me of wearing a damp scarf on a hot day.
Thanks to lyn67 for the link to the double Pretzel knot (which I believe has some other names too). That is also one of my favourite knots. Tied like this, the scarf stays in place even if you are moving around. And it covers more of your neck and chest, so it's a nice solution when you're in cooler surroundings.
I agree with Katerina and others that scarves are very useful travel items. And Katerina, thank you for reminding me that a scarf can even be used as an elegant top!
I practically always bring at least one thin scarf and one pashmina shawl even for a weekend trip. Often I'll let a patterned scarf/shawl be the key piece on which the rest of the travel wardrobe is built. This weekend, for instance, I chose a tartan pashmina shawl in turquoise & red & white & black as my key piece and let all the other travel items be in these colours.