It is great to be able to dig deep when big events occur in any big civilizational region in the world. I like to follow news that is related to my research and learn languages at the same time.
Google translate is invaluable for early stages of language learning this way (http://translate.google.com/#), as well as a good overview of grammar (e.g. http://www.ielanguages.com/languages.html). To find big news sources in specific countries go to: http://news.bbc.co.uk/2/hi/country_profiles/default.stm and click on ‘media’ in a country. For European countries you can also use: http://www.presseurop.eu/en/sources. For European languages, Euronews (you can listen to it in 13 languages) is also great: http://www.euronews.com/news/streaming-live/
A few further starting links for big regions:
Africa in French: http://www.jeuneafrique.com/
Africa in French: http://www.rfi.fr/afrique
Latin America in Spanish: http://www.informador.com.mx/14/america-latina
Latin America in Portuguese: http://oglobo.globo.com/
Eastern Europe in Russian: http://www.dw.de/%D1%82%D0%B5%D0%BC%D1%8B-%D0%B4%D0%BD%D1%8F/s-9119
Eastern Europe in Russian: http://www.kommersant.ru/
East Asia in Chinese: http://www.bbc.co.uk/zhongwen/simp/
East Asia in Chinese: http://www.chinese.rfi.fr/
East Asia in Chinese (state-run): http://www.people.com.cn/
South Asia in English: http://timesofindia.indiatimes.com/
Middle East in Arabic: http://www.aljazeera.net/portal
Europe in German: http://www.spiegel.de/
Europe (Hungary?) in Hungarian: http://hvg.hu/
Politakos 