I will start this off and hopefully some of our other members who are also consultants can help out as well.
I run an HR consulting company and do consulting myself. This is quite recent for me having been in big companies prior to this.
I have two documents. First is a traditional CV. I have this as jobs, key accountabilities (more for the most recent two and then one line for the others) and then bullet points of my key achievements (by job). It is crushed into two pages. I use this to demonstrate my pedigree. I do not often change this document - mostly because it is a real effort and one extra word throws it into three pages
Second, I use one page Bios. These are totally customised dependent on the project I am pitching for. I keep examples of all my achievements in a spreadsheet and cut and past them in. I also have 6 pre-made ones. Clearly the achievement bullet points of my bio include those on my CV but there is the opportunity to access a wider range.
Frankly I find this all a bit tedious. It is for that reason I am developing an application at the moment which will do this for me (and others if it takes off!).
I do know consultants who take a Skill Set approach to their CVs. Identifying the areas that they wish to demonstrate capability in and giving examples under each of these with a brief list of employers and jobs at the bottom. This can work well but I find that I want to cover too broad an area so it will not work for me on the CV. Effectively my Bios are 'skill set' driven. So for example I have on on Mergers and Acquisitions, another on business transformation and change etc
As you can see - by the lenght of this post - a topic which is dear to my heart. Delighted to hear how others approach this and why!