The task of topical classification of Web queries is to classify Web queries into a set of target categories. Machine learning based conventional approaches usually rely on external sources of information to obtain additional features for Web queries and training data for target categories. Unfortunately, these approaches are known to suffer from inability to adapt to different target categories which may be caused by the dynamic changes observed in both Web topic taxonomy and Web content. In this paper, we propose a feature-free flexible approach to topical classification of Web queries. Our approach analyzes queries and topical categories themselves and utilizes the number of Web pages containing both a query and a category to determine their similarity. The most attractive feature of our approach is that it only utilizes the Web page counts estimated by a search engine to provide the Web query classification with respectable accuracy. We conduct experimental study on the effectiveness of our approach using a set of rank measures and show that our approach performs competitively to some popular state-of-the-art solutions which, however, make frequent use of external sources and are inherently insufficient in flexibility.