Yes, you can watch live sports online for free. There are many websites that offer free live sports streaming. Streamsports.me, wiziwig.tv and FirstRowSports are just a few of these sites.
The streaming on these sites will generally not have the same level of picture quality you would get when watching a sporting event on a television. Also, these sites make money from advertisements, so you may need to sit through some advertisements or close them out in order to view the game that you wish to watch. Some of these sites also offer free live TV streaming or free movies.