Box-office figures for major films currently in release are pretty easy to obtain, as most entertainment news sites carry headline figures. For free sources, your best bet is probably Google. If you are looking for more in-depth figures or those for a specific territory, then any of the trade magazine sites is probably a good starting point.
VarietyThe Hollywood ReporterScreen InternationalOf these, The Hollywood Reporter has the most extensive free content, although detailed box-office figures are subscriber-only.
For historical figures, you’re entering an area of the business where is it very difficult to obtain information for free. Maintaining databases and creating access to them does not come cheaply so most services levy some kind of fee (either for one-time access or on subscription basis). You can check out the following sites:
Box Office GuruBox Office MojoFilm TrackerInternet Movie DatabaseThe NumbersProjectionzShowbizdataFinally, if you’re interested in data for a non-US film it’s often worth getting in touch with the national film commission (or similar body) for the country where the film was made. Because the film industries outside of the US are generally much smaller, national film commissions tend to be much more plugged in to what is happening with films from their country.