It depends on which country you are trying to target, but for the UK, the answer is essentially no. Google has more than 90 per cent of the market, with the rest mostly going to Yahoo! and Bing (and even on those two, “Google” is the most popular search term).
Things are different in other countries. For example, in North America, Google’s share is about 65 per cent. However, there are only a handful of major markets, such as China, where Google is not the dominant player.