"A work that is no longer copyright protected is considered to be “in the public domain”. It should be noted, however, that photographs of works of art in the public domain may themselves be copyrighted and will likely require a license for publication, even though the public domain works which are the subject of the photos are no longer protected."
[Definition from ARS, the Artist Rights Society]
In some cases you can use a work that is not in the public domain without seeking permission. This is known as "fair use."
Four factors to be considered in determining whether or not a particular use is fair:
1. The purpose and character of the use, including whether such use is of commercial nature or is for nonprofit educational purposes
2. The nature of the copyrighted work
3. The amount and substantiality of the portion used in relation to the copyrighted work as a whole
4. The effect of the use upon the potential market for, or value of, the copyrighted work
Although Section 107 of the Copyright Act includes teaching, scholarship and research, along with making "multiple copies for classroom use," as among the uses of copyrighted works that may qualify as fair use, none of these uses automatically qualifies as a fair use.
[From the U.S. Copyright Office explanation of fair use]
Since most images are still available only in print form, it is generally considered fair use to scan one for educational and scholarly use. (See the Duke University research guide.)