Most people cool their wort as quickly as possible after the boil. This has 2 main benefits: cooling the wort helps separate out the cold break (which I think are some sort of proteins, but not totally sure the specifics), which results in clearer beer, and also the faster you cool your beer, the sooner you can pitch your yeast, which means the sooner alcohol starts forming, and the less chance there is for wild bacteria to start infecting your beer.
You don't need a wort chiller to do this - you can use an ice bath or a zillion other techniques. The main advantage to the wort chiller is that it is fast (you can cool your brew in 15 or 25 minutes depending on size and other factors), simple to use, and means you don't have to keep buying/making ice each time you brew.