Honestly, I just use a Google sheet (spreadsheet). Columns are: Date, Job Title, Company, Job Level, Website Applied Through, Expected Response Date (calculated based on an average response time which is about 2 weeks), Initial Response Date, and then multiple columns for date and description of each interaction.

I'm sure there are automated tools for this kind of thing, but I prefer the manual method as I can control and manipulate the data more. I have other columns for counting being turned down, counting response types and counting interview types.

It might sound more complex than it is.