YouTube has a special page at youtube.com/trailers where you can watch movie trailers of many upcoming releases as well as movies that are already running in theatres.
Movie studios and fans have been uploading video trailers on YouTube for long but this page makes it easy for you to quickly spot the “official” trailers from one place without having to use search.
YouTube currently aggregates trailers of mostly Hollywood release though I did spot one from an upcoming Bollywood release as well. The “latest trailers” in the sidebar will help you discover new movie trailers that may have been added since your last visit.
Apple maintains a hugely popular movie trailers website at trailers.apple.com but it requires the QuickTime plug-in while the YouTube trailers require the Flash player which most of us already have on your browsers.