Citing ArcGIS Desktop when writing papers?

There are formats for citing software, see for example this question on tex.SE. Whether you should cite them depends on the publication venue, but particularly where the specific implementation is non-obvious it is a helpful thing to include. In this case, the citation would look something like:

ESRI 2011. ArcGIS Desktop: Release 10. Redlands, CA: Environmental Systems Research Institute.

I might be misunderstanding your question but, I don't think you should cite ArcGIS or any of the tools used in any analysis. Citation is used for authoritative sources. Data citation should be included in the metadata of your data source. The tool you use for analysis is not an authoritative source, the person using the tool is. E. g. you cite the author of an article or book, not the pen it was written with.

In order for another scientist to replicate your work in an independent manner, you need to specify the algorithm you use at least and preferably provide a link to a publicly inspectable source code repository. Imagine if chemists wrote papers saying you must get your reagents from X Supply House to repeat this.