I've done it before with various types of pickle, with decent results. Generally the 2nd batch isn't quite as good as the first, but I'm usually lazy and just throw new veg in the brine (cukes, beets, brussel sprouts, whatever the case may be) without boiling. Straining, adding new pickling spice, and reboiling would probably help the end product.
Of course, there are also plenty of other uses for the leftover vinegar (think salad dressing, bloody mary's, etc).
Bottled/Drinking: Apfelwein, Graf, Leaping Goats Coffee Brown Ale, Favorite Season Farmhouse Ale, Anniversary Barleywine, Hop House Saison, Something Blue-berry Saison