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It depends. I used to dump it. Now I tend to drink it.

I don't stir it into the yogurt because that makes the yogurt runnier, by breaking the rather delicate structures yogurt forms itself in culturing. Now, with commercial yogurts, those may already have been destroyed by blending after culturing and before packaging at the factory - only yogurts that are fermented in the cup have the natural structure - factory-blended ones tend to use cornstarch or other gels to make the product firm instead. 

I will rather deliberately dig a hole in one side of a large tub of yogurt to drain off whey and make the remaining yogurt firmer. By the time I get to the bottom of a quart/litre tub, what's left is up there with "strained" (or "Greek") yogurt if starting from regular yogurt. It's firmer yet if starting from strained yogurt. I rather like that. If you didn't want whey to separate in the first place, attempting to leave the top surface _as flat as possible_ when removing to serve will help with that, but not require stirring the yogurt and making it even more liquid/runny.

I suppose I should acknowledge that apparently some people like runny yogurt. I'm not one.