Software programs that can be legally copied and shared at no cost are categorized as what type of software?

The correct categorization for software programs that can be legally copied and shared at no cost is freeware. Freeware is specifically designed to be distributed for free, and users can share it without needing to pay for licenses. This type of software is generally available to anyone, with no restrictions on the sharing of the original version.

Shareware, while also involving free distribution, typically has a trial period or limited features. Users are encouraged to pay for additional functionality or extended use beyond an initial trial, making it distinct from freeware, which is completely free to use indefinitely without a cost.

Open-source software allows users to not only use the software for free but also to modify and distribute their own versions. However, this definition is more about the accessibility of the source code rather than focusing solely on cost and copyability.

Proprietary software, in contrast, is protected by copyright and typically requires the purchase of a license. Users cannot legally copy or share proprietary programs without permission.

In summary, freeware stands out as the correct answer because it is available at no cost and can be shared legally, aligning perfectly with the description given in the question.