I used to never sort my laundry at all, largely because I never use anything except cold water to wash clothes, until I realized that most of my clothes last longer (or at least, look nice without shrinking for longer) if I hang dry them.
Since my husband can't remember which of my clothes get tumble dried and which get hung up, he asked that we sort our laundry into two baskets (one for hang dry, one for tumble dry). It's definitely been useful for us, since you don't have to dig through a single clothes hamper to pull out the clothes you can wash in one way or another, or dig through a pile of wet laundry to pull out what can't be dried (inevitably missing something in the process).
Until recently, that was the extent of our sorting (which basically just means tossing our dirty clothes into the appropriate hamper as we take them off). We always washed sheets and towels separately, in part because they are a load all by themselves, and in part because the towels produce massive quantities of lint always.
I also didn't used to own any white clothing that was meant to be actually seen until a few months ago. My white dress shirt has gotten noticeably dingy, even though I've never actually stained it, just because it gets washed with colored clothing. I broke down and bought some hydrogen peroxide bleach and soaked it and some other whites for just a few hours over the weekend, and it's already noticeably brighter. Because of that, we're going to start washing whites separately so that we can keep them white. Most of what we own that is white will just be filler for that one white dress shirt (since socks and undershirts and washclothes don't really need to be bright white), but it's become necessary.
Given that I now have all this overnight soaking to do, though, I'd really appreciate having a laundry sink to do it in. Too bad I just have a closet in my bathroom with my washer/dryer and clothes hampers.