There are some. Neeva is one I've heard of, and there was another similar one mentioned on HN just recently that I've forgotten. There was also Cuil. Bing exists of course. And then there are the language specific ones, Yandex, Naver, Baidu, and others I'm sure. And that's just the ones that make their own index, there's a sea of competitors like DuckDuckGo and StartPage that mostly license results from someone else (including Google). And there are also verticals with competitors like Amazon for products or Yelp for food, which Google very much considers as competition.

As much as people claim otherwise, it's not that Google has no competition. People are trying! Google's product is legitimately good, despite the widespread perception of declining quality.