Google is just one search engine.
Several years ago, there were many, including Ask Jeeves, AltaVista, Yahoo, etc.
They all got a bit complacant though, and didn't spend that much time really improving the service they provided. Google came along and ate into their market, so much now that many people simple think of Google as _the_ search engine.
Microsoft have had a search engine for years now called Live Search. Bing is just a re-launch (with some improvments), of this service. It's just another search engine.
Competition is always a good thing, but so far, I see no reason at all why I'd switch from using Google. Bing is a very typical Microsoft product.
Try it, if you prefer the way the results are laid out, or anything else about it, then use it. It's just another website. Use Bing and Google if you want, and see if either gives you better results.