Micro Observatory
The Micro Observatory Robotic Telescope Network, operated by the Harvard Smithsonian Center for Astrophysics with support from NASA, is the most simplistic service here. It relies on a network of automatic 6-inch reflectors along the east and west coasts of the US, each equipped with a CCD camera. As it’s aimed at beginners and students, it is free to use.
The service does have limitations. You do not have real-time access to the telescopes, but instead schedule ‘jobs’ that are automatically distributed to the telescopes depending on capacity. You can only select from a limited list of objects, comprising planets, the Moon (if visible) and a handful of deep-sky objects. There is a limited choice of four different exposure times and whether you would like to use a filter or not. The images are available as GIFs or in their raw FITS format via a common directory on the project’s website.
There is still an older ongoing project that allows you to set some more detailed parameters, but for this you have to register and propose a research project. The proposals are reviewed three times per year.
PROS: Good starting point; free and easy access CONS: Limited flexibility; images are often poor quality