What is the equivalent of the laboratory notebook in the humanities?
I asked my wife, which works in art history/egyptology. So first, "it depends of how the person works" ;).
However, it seems that many people are making a large number of thematic reading synthesis, research notes (as we do) and she also pointed out the importance of her personal database, where she stores archaeological artefacts, their descriptions, the related bibliography, personal notes about them, their relations, etc. According to her, this is THE most important thing for her work.
From my impression, the nearest equivalent would be an academics' text source repository. This could be a library of theoretical works personally owned (and almost certainly monographic rather than papers). It could be a set of commonly referenced canon texts spread across four or five libraries in their region that they consult. It could be the items above plus documentary series such as archives, cultural texts.
The objects manipulated, day to day, in conducting humanities research are texts; whether these are straight texts, or the meanings developed from physical records, or the meanings developed reflecting on terse problem statements.
In my experience, some scholars keep detailed notes, and others don't. I try and keep my notes and sources in a deep text searchable database with what meta-data I can cheaply acquire. There is no standard for keeping a repository, and the way in which a scholar learns to keep an adequate repository is idiosyncratic.
There isn't a disciplinary standard for keeping a repository, above and beyond "study skills" type courses which aren't mandatory or systematised. To evidence of the adequacy of the "experiment" equivalent scholars demonstrate their mastery over the relevant texts by providing evidence of firmly supportable readings through citation and footnoting, or by quality argument.
Personally I've not heard of a dedicated "research notebook" in my discipline history, as may be used in the sciences. Like Sylvain Peyronnet's answer it very much depends on how a person works.
In history, as Samuel Russell's answer alludes to, most of a person's ideas or arguments are gleaned from primary documents. Because of this it becomes very important to be able to keep a track of the primary documents that may be relevant to your area of research. Personally I use Mendeley to keep track of everything and the notes/annotations I make in that go someway towards forming my research arguments later. I note though that even the use of software like Mendeley is not common in my department.
I believe one of the advantages of the research notebook is that it can keep track of when work was conducted by date, something that I have never heard mentioned in the Humanities. The disadvantage of this is that there is no way of proving when you may have had an idea based on your readings.