Pickling Liquid

Two words: bloody mary!

You can drink it. Sometimes pickle juice really hits the spot (electrolyte deficiency can do that).
Otherwise I would toss it, pickling brine gets watered down by the vegetables that are in it, so it doesn't have as much flavor and has a different acidity and salt content by the time you've used the pickles, it is no longer useful for making more pickles.
I have used pickle juice in salad dressing (creamy with mayo) and I've used leftover commercial pickle liquid to quick-pickle hardboiled eggs, so I guess depending on the flavor those could work too.
You might be able to use it as weed killer depending on what's in it.

Apparently you can use it to brine chicken for fried chicken. Go to SeriousEats.com for the Chik-Fil-A-esque chicken recipe there's lots of mention that the brining liquid for their chicken contains pickle juice.