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." U.S. patents and applications 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." Strong keyword searching. Also available with a simple interface: "Google Patents" --- https://patents.google.com.
For U.S. patents and applications. "Basic" and "Advanced" search options. "Advanced" is based on the advanced search tool used by the U.S. patent examiners and is daunting for first-time users. "Basic" is more approachable but has only a few search fields.
"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.