I think the best use of these is when you are wanting to look at performance of one particular thing.
The best display of the usefulness of these charts I think is probably the sports statistics examples where you are looking at overall performance of a player or team shown in this example:
http://howtowatchsports.com/spider-graphs-charting-basketball-statistics/
The reason why I think it is useful is because all of the values that are measured use the same method of measurement (a ranking from 0-100). It clearly shows strengths and weaknesses and would be useful for a basketball coach to decide where they should put each player on the court and in which areas their players need more training. You can apply the same type of radar to judge performance of employees where their team leader rates them on in different areas of their work, or maybe for customer feedback where customers give a rating for different aspects of their experience at a store.
They can also be used well for very quick identfication of outlier values but I find it is very rare that you will have so few outliers that this would be more useful than using a scatter graph instead which allows you to easily identify a lot of outliers easily.
I think those radars that don't use the same form of measurement for each item in the radar are misleading because a value may be high for an item but appear low because it is warped by an item that has a much larger absolute value and is unrelated eg. a percentage and a money value.
Radar charts that have a large number of steps (eg. money) from the center to the perimetre I feel are not very useful either because it is much harder to read gradual steps compared to a bar or a line.
Radar charts that have a dimension, which causes layering of multiple lines over the plot I think are not very useful either because they are just too damn hard to read, the lines overlap each other and are close to each other which makes it extremely difficult to compare. If there are only 2 lines in the dimension (eg. 1 line for one player vs 1 line for another player) then it is probably ok, but more than 2 lines and things start getting confusing.
Radar charts that use time as a base to measure traffic (eg. visits to a website) are pretty useless as well because you are always going to have pretty much the same same results with very little movement. People browse the internet more at certain times during the day so you will just see exactly that on the chart, nothing you change in your business is going to make much difference to that so it is not useful to you.
