On my Conworld, the oceans are purple. This is mostly for aesthetic purposes and my current explanation is an abundance of cyanobacteria. I'm not sure that this explains it correctly, so what could explain this realistically? The water doesn't have to be potable, because a scarcity of fresh water is one of the intended characteristics of the conworld.
There's any number of reasons why. While pollution, plankton, and phenolphthalein all work just fine, I'd like to suggest a different perception of color.
For example, ancient Greeks had a much different definition for the color blue, and interpreted the ocean as green or purple. In fact, in The Odyssey, Homer describes the sea as "wine-dark." Perhaps the inhabitants don't have a word for the ocean's color, and interpret it as purple?
If a concrete reason is truly wanted, you could also place a purple mineral in the water. Azurite or Quartz could work, but this would only make shallow areas look purple, and if in a bucket or similar, it would appear clear again. My suggestion would be high quantities of aluminum potassium sulfate and chromium potassium sulfate in the oceans. This would have the side effect of creating purple crystals in shallow areas.
One real possibility is the same thing that makes wine purple: tannins and anthocyanins.
Our ocean is salty because of literal eons of rivers carrying minute amounts of dissolved solide to the sea, where there is no outlet, so evaporation very slowly increases the salinity (our bodies are less saline than the oceans, say biologists, because our distant ancestors fixed their intracellular water salinity when the sea was less salty, and the sensitivity of the whole life process requires maintaining it where it was most of a billion years ago).
If, sometime in that billion years, there arose a widespread producer of tannins and anthocyanins (perhaps a form of phytoplankton?), those organics would dissolve into the ocean water just as they do when a forest brook flows over oak roots or leaf mats.
Wait! Oak tea is red-brown -- and so it is (so is ordinary tea, for that matter), because tannic acid is brown in solution. Why is wine purple instead? Almost all wines contain traces of blue pigment from the grape skins (the anthocyanins) -- and the more tannin is present, the more we can see this combined color of the anthocyanin (otherwise nearly invisible) and the tannin.
Now, in sea water, the concentrations could be so low as to be invisible in small quantities -- dip up a wine glass of sea water and it'll look like, well, water. But get it a few meters deep, and you'll start to see the color. Get it deep enough for our ocean to start looking green, and it'll start to look like wine.
An additional quality this sort of sea would possess is that different climates would show different amounts or even hues of color. The polar seas might be extra dark, like burgundy (because high nutrient levels in the water), and the equatorial would be light, like a Reisling, because the waters are much "cleaner".