TheOptimizationIdiot - 8:47 pm on Apr 10, 2013 (gmt 0) [edited by: TheOptimizationIdiot at 8:50 pm (utc) on Apr 10, 2013]
...don't know if you'd canonicalize index.html to "/" since that alone is index, no matter what you name the index page - hope that's phrased right for everyone ...does not compute....
There's no reason not to if you have a preferred version to be displayed but can't use a 301 for some reason. Many sites can use a 301 and "strip" the index.ext via external redirect so there's only one location for the information physically available, but if you can't redirect, I would think that's a good use of the canonical to indicate which version (dir/ or dir/index.ext) should be shown in the results.
If you don't have a preferred version, then it's no big deal to not use it, because Google will just pick one themselves to treat as the canonical. Using the tag really just gives you more control over what URL is show in the results when there's multiple choices for the same or essentially the same information.
[edited by: TheOptimizationIdiot at 8:50 pm (utc) on Apr 10, 2013]