Google Trends allows you to analyse global web search trends since 2004. You can explore multiple search trends and compare them on a customizable chart. You can fine-tune your analysis by the time, location and category of the search data. In addition to Google Search this tool also gives access to YouTube, Google Images, Google News and Google Shopping statistics.
Social Mention aggregates user-generated content into a single stream of information. This is a search and analysis platform that allows you to track and measure what people are saying about you, your company, a new product, etc. The analysis is based on English language data and the results can be downloaded in Excel.
Next Big Sound provides social media trend analysis with focus on music brands, ie. bands, artists, tracks. Their proprietory algoriothm reveals not only recent trends but also predictions on what is expected to happen in the music industry. The freely accessible part of the site provides charts, but does not allow customized analysis.
App Annie is utilizing mobile app store download statistics and some other related sources to analyse trends in mobile app business. This allows developers to better target their efforts. The app store and app analytics charts are freely available for registered users and provide a few interesting and customisable views.