Robert Hanson Hansen, also known as Butcher Baker, would kidnap women, fly them to a remote location, rape and strip them, and gave them a head start. He would then track the woman and kill her with either a hunting knife or a rifle. He described it as going after a bear or trophy sheep in his confession.

It was written about in Butcher, Baker by Gilmour & Hale and The Anchorage Daily news has/had lots of coverage.

I'm not a historian and I know I'm late, but I just found out about this today and think it's important to remember these crimes. British colonialists hunted Aborigines in Tasmania for sport. Quote by UCLA professor Jared Diamond:

"Tactics for hunting down Tasmanians included riding out on horseback to shoot them, setting out steel traps to catch them, and putting out poison flour where they might find and eat it. Sheperds cut off the penis and testicles of aboriginal men, to watch the men run a few yards before dying. At a hill christened Mount Victory, settlers slaughtered 30 Tasmanians and threw their bodies over a cliff. One party of police killed 70 Tasmanians and dashed out the children's brains."

Here's a paper on it, the 3rd paragraph on page 9 calls it "pursuit killings".

Can you elaborate some more? I mean there are things like this but that was during wartime.

If you mean something like watching it happening like a game of baseball then would you consider certain events in the Colosseum/Amphitheater (particularly the ones which were actually made to be more of an execution) to be sport played in peacetime?

Someone on here posted the other day about a widely publicized competition in Japanese occupied China about two officers who competed to see who would be the first to kill 100 people with a sword.

http://en.wikipedia.org/wiki/Contest_to_kill_100_people_using_a_sword