Water is the most important thing in any worst case survival scenario. Without it, you'll be dead within a week. Clean water is just as important. Clear rivers and lakes may look clean, but there are millions of organisms in fresh water. If you don't purify it, you can get extremely sick from bacteria or viruses. Freshwater springs can be safe to drink from without filtering, but in a survival situation you should err on the side of caution.
Boil water for at least 10 minutes to avoid waterborne disease. Rainwater in most rural areas can usually be consumed without risk of disease or illness as well, so catch some if you can. Sadly, most areas of the earth are touched by litter. Use this to your advantage -- look for an aluminum can, glass jar or a large seashell to boil water in.
Another way to purify water is with purification tablets. The tablets use either iodine or chlorine to treat the water. Murky water often needs more than one tablet to make it safe, and any tablet needs at least 30 minutes to be fully effective. Like with boiling, it's best to give the water an initial straining with some kind of cloth. It's also safer to drink warmer water, so if it's from a cold mountain stream, allow it to heat up a little in the sun first.