It depends. If you are looking for a single-workstation solution libreoffice base should be sufficient. If you are looking for a network-capable System, so several people can access and work on the data from different workstations or other machines, I'd recommend PostgreSQL as Database Management System, with e.g. libreoffice as frontend for data-entry and manipulation. PostgreSQL has many advantages:

- it is open software, so you can have it for free, no license cost, complete control of what happens with your data under the hood

- it has been developed for a long time and has a mighty community therefore it is reliable and support and educational material is easily obtained from the community

- it can handle geographical data via the PostGIS extension directly in the database, so your artifacts can be displayed, entered, manipulated and analyzed with a GIS software like QGis

disadvantages:

- it is a professional DBMS and not as intuitive as MS access or libreoffice base, you will need dive a little deeper into SQL and Database Management or get some help from a database-expert

https://www.postgresql.org

https://www.postgresql.org/docs/manuals/

http://postgis.net

For your use-case, I would say MongoDB.   The data can be put there in JSON data format, and there is no need for a schema.   The disadvantage is that it doesn't force you to model the relationships between objects - if that is in an issue, you might want to look at MySQL.

"Best" is dependent upon a number of things.  The greatest issues with archaeological cataloging systems are more about the actual design of the database than about the software employed to implement it.  For an office or laboratory environment dependent on Windows OS and proprietary software, Access is more than adequate, if potentially costly.  It has very good report generating capacities and integrates well with Excel.  Other databases operating Windows environments including MySQL, Oracle, and Postgresql implement SQL DBMS systems that are highly reliable and vary from free and opensource (postgresql, MariaDB, etc.) to extraordinarily expensive (Oracle).

If you have the time to spend learning the ropes, Postgresql, or Mariadb, and LibreOffice offer the same general tabular and analytical output quality, but demand intense study and skill development.

Many archaeological cataloging systems, especially in smaller operations, employ an immense, flat-file approach that rolls together the critical accession information, which all archaeological cataloging systems must contain,  with analytical data.  The latter are likely to be ephemeral and subject to repeated alteration as different analysts examine the same artifacts.  If that data is contained directly in the primary catalog, the catalog itself is potentially subject to catastrophic accidents through operator errors and even a highly knowledgeable operator can make monumental mistakes if rushed.  One type of program that should NEVER be used for a catalog is a spreadsheet.  While the latest iterations have overcome the problems of earlier versions, analytical summaries are still subject to range errors accidentally introduced by the user and unless the user has a very good understanding of just how the output from analysis should really look, errors that "appear" to be reasonable can creep in . 

I would suggest to look into CollectionSpace. It's a server app used by several large-scale museum (e.g. Phoebe Hearst Museum - UC Berkeley).

https://libreoffice.org/discover/base/

CDS/ISIS

MobiDB database available on iOS, Android, Windows. Synchronizes database through Dropbox, OneDrive, Google Drive. No need in central webserver and etc. Excel export is also available. It's a perfect fit for artifact cataloging and works fine in the field.

I'm glad this question has been viewed so many times and thank you all for your responses, which continue to be intriguing. Since I posted this question nearly three years ago, I developed an Access Database with the file saved on our network server. I am extremely happy with it. Especially the Form I created, with drop down options. Did all of over a weekend with the help of YouTube.

Today we have up to six research assistants cataloging and analyzing lithics, fauna, and flora simultaneously at individual work stations and I am able to also work in the file at the same time from my office. It has been extremely productive. The reports and ability to plug directly into GIS is also very useful.Mostly, I export filtered results to Excel and plug that into Surfer for excavation maps.

For something ultra-light, I love to use Airtable

From an Apple-user perspective looking to catalogue image capture and GPS data for site documentation, do the improvements on recent FileMaker outweigh the fact it’s not free? Was able to create custom apps for iPad a few years ago with the idea of using it in the field with multiple users real-time. This link for version 19, with exciting new features, might shorten the learning curve..

https://m.youtube.com/watch?v=lwN_Tp5iOEs

Dear Brian, I think Shannon McPherron's E4 or E5 program is interesting within the topic you mention. You can easily define what variables you want to measure and the program allows to fill the database consistently. E4 generates a mdb file, E5 is a new upgrade that uses JSON data and available export to csv.

I agree with Petr Neruda above that the E4 program (FAQ and download here: https://www.oldstoneage.com/osa/tech/e4/; the beta of E5 can be found here https://pypi.org/project/e5/) is a great and easy way to analyze finds, such as lithics which I have done before. Generally, I mostly use a custom-built Access version to analyze artefacts because the queries are a great and efficient way to do analyses and get simple summary statistics, plus it can easily be integrated and linked with on overall excavation database. Yet, I always encourage students (and myself) to stay active and agile, e.g. checking out different software and seeing which program works best for which kinds of artifacts, assemblages and questions!

We use the E4 software developed by Shannon McPherron and freely available on Old Stone Age site https://www.oldstoneage.com/osa/tech/e4/

That is a tricky question. Modern "catalogs" carry a great deal more function than any archaeological catalog did prior to the widespread use of computers. In addition to the basic descriptive information unique to a specific lot in the catalog, many catalog systems now include analytical data at various levels of specificity. Systems are also very limited in how transparent they can be. Field names are rarely as transparent was we would like them to be. Analytical codes similarly lean toward increasingly obscure as your data volume increases and numbers of unique items, or observations of special conditions demand modified coding for specific artifacts. If, for instance, you excavate a specific volume from a specific provenience, and that yields 500 pieces of debitage of varying completeness and technological diagnostics, do you catalog each piece individually (do all the analysis as the material is catalogued - nearly impolssible), or do you catalog the lot, and schedule analytical data collection later. Do you store that information in a single immense flat file, or do you employ a relational design?

I've preferred to design the catalogue system as a retrieval system that allows the easy location and retrieval of the actual material. Analytical data can be related to the catalog if desired or necessary through tables keyed by id numbers or other characteristics. Also, many museums or curatorial facilities will have specific standards regarding the content and format of the catalog, and if computerized, what program is to used.

You can try FileMaker pro.

You should use Ishtar ( https://ishtar-archeo.net/en/ ) :) it was designed for that.

Import/export with quality and mapping etc.

Dear Dr Brain

The choice of the best database software for artifact cataloging depends on several factors, including the specific requirements of your project, your technical expertise, budget constraints, and the scale of your artifact cataloging efforts. Here are a few popular database options that are commonly used for artifact cataloging:

When selecting a database software for artifact cataloging, consider the following:

• Ease of Use: Choose a solution that aligns with your technical skills and the skills of your team.
• Scalability: Consider the potential growth of your catalog over time. Will the database be able to handle a larger number of artifacts?
• Customization: Depending on your needs, you might require a solution that allows for extensive customization of data fields and relationships.
• Collaboration: If multiple people will be working on the catalog simultaneously, a solution that supports collaboration is crucial.
• Data Security: Ensure that the chosen solution provides appropriate security measures for protecting sensitive artifact information.
• Budget: Some solutions are free or open-source, while others come with licensing fees or subscription costs. Consider your budget constraints.

Ultimately, the best database software for artifact cataloging will depend on your unique requirements and resources. It's a good idea to evaluate a few options, possibly through trials or demos, to determine which one aligns best with your project's needs.