Who would win a fight between....A contentious question, especially on the internet. No matter the subject, you will find supporters either way. Batman versus Superman was the first debate of real contention I encountered. The amateur, of course, picks Superman, who after all possesses many powers that Bruce Wayne does not. However, this fails to note history, and the fact that Batman is always prepared. This argument can continue on for many pages.
There are websites devoted to battles between star trek and star wars (the answer is wars, simply because star trek cares slightly about physics, and star wars does not), where information is carefully considered and compared in a manner that greatly disturbs.
A vs questions is important to set up carefully. Putting Chuck Norris against a wimpy opponent like skeletor is a mistake, for example (roundhouse kick to the face!) I would certainly argue that the Bear vs Shark issue is one that is not particularly balanced- surely the shark would have the advantage against the bear, too deep in the water too move?
So, for your delight and deliberation, heres some vs.
Chuck Norris vs Jack Bauer
Jesus vs Santa Claus
Abraham Lincoln vs Churchill
Blackadder vs House
Optimus Prime vs the Terminator
Mary Poppins vs Alice (of wonderland fame)
Peter Pan vs Jack Sparrow
Bill Gates vs Thomas Edison
...thats probably enough for now