The searchable database of the European Patent Office. According to the website, "Espacenet is accessible to beginners and experts and is updated daily. It contains data on more than 100 million patent documents from around the world. Supporting information can help you understand whether a patent has been granted and if it is still in force." U.S. patents are included here.
Google for patents. From the website: "Patents from around the world, translated. Plus technical papers and books, organized and labeled automatically. Search for prior art, all in one place." We especially like it when keyword searching. A frequently-expressed concern about the database is that Google does not explain details of coverage.
Database of the U.S. Patent and Trademark Office containing U.S. patent applications. U.S. applications are not always made public but were never made public before 2001. (Since we assume that a granted patent reveals much of the application, this might matter only for an application which did not issue as a patent.)
"The PATENTSCOPE database provides access to international Patent Cooperation Treaty (PCT) applications in full text format on the day of publication, as well as to patent documents of participating national and regional patent offices." Recommended for the patents of smaller countries whose documents might otherwise be hard to find.
Here you can see U.S. application materials as well as communications between the examiner and inventor (or attorney). This is the older interface, expected to be replaced by the "Patent Center" interface.