Most local search engines cater to a special market or specific groups of products or services. There will always be a demand for easy reference especially if the industry covers a wide array of offers/categories and areas. This is specially true for industries like travel, hotel, reataurants, home/real estate, etc.
Take for example Baidu, this is the most popular search engine in China, with 80% market share while Google China is just a runner-up.
Students I know still use Ask.com for their assignments.
SearchTempest is a search engine for online classified ads from Craiglist, ebay and Amazon, etc.
There are the emergence of pro-privacy search engines like DuckDuckGo, Hulbee.
In general, Google may still be the popular worldwide search engine worldwide but there will be other companies who will find opportunity in niche marketing and build a reputation based on their specialty. This is target marketing catering to specific markets and must be supported by related companies who wish added exposure to their business.