Which process mapping software does your organization use to map out current processes and future workflows?

For the high level process alignment, we do this using the ArchiMate modelling language (in Sparx Enterprise). The moment the process needs to be defined more in detail, we use BPMN notation, and generally using Visio (although I've seen people use draw.io-alike plugin in Confluence for this as well).

We use Visio, but increasingly are moving to MermaidChart. It enables us to generate models from AI. It's not the prettiest output, but is it ever fast when you've chained prompts to analyze a current process, identify waste, redesign and spit out the final workflow.

Also works well with data flows, sequence diagrams, ERDs, etc.

eraser.io

SAP Signavio is used to define business processes.  

We use ViziBPM from Elca / Switzerland.
It is an application over Visio, fully compliant with BPMN 2.0. Errors an warnings on diagram, where it breaks the BPMN standard, are included.
Our preferred feature is that it allows the use of a proper designed MS Word template to create full documentation of the process. For proper designing it uses specifications in hidden text in template. It extract all sort of information from the process (not only the diagram) in our specific format and order. We create and manage entire procedures in VizBPM.
Another feature we like is adding a report of the quality of diagram design, based on Bruce Silver specifications.
I think (tested in early versions of ViziBPM but not tested in recent versions) that, if you create a BPMN 1.2 (not 2.0) compliant diagram, you can simulate the process with the right information given (effort, use time, waiting time etc.) and see in its reports where are the bottlenecks, the effort per activity and other parameters.
Excellent for design and maintenance, imo.