My first thought was the blue passenger pigeon. There were billions of them, and flocks filled the skies over the U.S. until they were over-hunted in the 19th century, used not just for food, but also ground up for fertilizer and shot for fun. The forests in which they bred were also cleared by humans in order to build settlements. The last one died in 1914. That was tragic because it was so irresponsible and unnecessary, the destruction of one species by the reckless stupidity of another - one that is supposed to have brains.
However, looking at this question another way, what animal would be useful to have around again, I think maybe a tame tyrannosaurus rex might be pretty useful to sort out some of the human beings who are around today. He'd have to be well trained, though, and happy to walk on a leash.