I always cut away parts of the map that I do not need. But I make sure to leave parts that I do not plan to visit but may have to use in an emergency; such as houses, roads and small communities. On longer walks when you may need to use many maps, this practice can save a surprising amount of weight and space.
I usually impregnate my maps so that they will not completely dissolve in prolonged rain in the middle of somewhere. For environmental reasons I prefer a waterbased sealant, like the one on the left above.
I do not carry anything but a whistle in my pant pockets these days. Folded map, compass and GPS travel in a pouch on the waist-belt of my pack. A compact camera often lives in the same small compartment.
Comments and current insights: I find maps completely covered in plastic to be unwieldy. However, maps printed on plastic or Tyvek can give you a map that lasts for a very long time. For country in which you travel a lot, a hard-wearing map is a good idea. I have learned not clinging on to old maps too long. Even if the mountains and rivers stay the same, roads, houses, mountain huts, bridges and other features, which may be important for security reasons, tend to change. In the future, maps might be completely electronic and contained in GPS devices or telephones. But as long as battery power is not entirely reliable on all occasions (long trips, cold weather) I think the map as we know it will be used for quite a while yet.