Although bibliographies are not
legally required, especially if sources are cited in the text of a work, academic publishers and respected mainstream publishers generally do require them as a matter of
policy. Although unethical, plagiarism
per se is not illegal unless it also involves copyright infringement. For example, as plagiarismchecker points out,
William Shakespeare's plays are not copyrighted because they're too old [i. e., they are in the public domain]. Even though it would technically be legal to copy from one of those plays for an English assignment, it would still be plagiarism if you didn't give credit to Shakespeare. Your teacher may not be able to take you to court over it, but she can certainly give you an F. You might even get suspended or expelled from school. Even though copying one sentence from a Web site is legal according to United States copyright laws, that may still count as plagiarism in your teacher's book.
To be safe, it is always best to cite sources in the text (body) of the work and to provide full publishing information in the format required by the discipline involved (e. g., Modern Language Association, American Psychological Association, Chicago Manual of Style, etc.).