In reply to Fredt:
I have regularly used a half rope for glacier travel with the other half rope in a rucksack ready to get out on a more technical route. Sometimes I use a triple rated, as Toby mentions, with a half rope stored as above or just by itself on many routes. I have also used a single half rope or triple rated rope on easy (for me and partner) scrambling / moving together ground. However, there are times when I prefer to revert to a thicker single rope.
1) If the rock is especially abrasive / sharp and I am using a lot of direct belays or weaving in and out of pinnacles. ( Some New Zealand routes have trashed my ropes very quickly )
2) When the odds of falling into a crevasse are heightened due to conditions, location, time of day, weather etc. The extra thickness makes it much easier to grip / handle especially with gloves on. For example the dry conditions in Cham. at the moment.
3) If I am climbing with someone on moving together ground who is less experienced / confident / capable on the ground.
As so often, I feel there is not a definite black and white answer but personal decisions and responsibility based on the people, route and conditions.