Keep in mind that there is no strict definition for what a genus is. In systematics, the only real entities are species and clades; what we call a genus is a clade consisting of a number of closely related species. The extent of these clades can vary wildly even within families - one genus is not equivalent to another genus just because they share the same Linnaean rank. They may very well differ substantially in age, diversity and genetic variability.

Although arbitrary 'species thresholds' have been proposed for taxonomic interpretations of DNA barcode data, there is no universal figure that can be usable within a broad taxonomic group. Within insects, a 15% gap would indicate deep divergence within, say, Lepidoptera, but not so much for other groups (e.g., lice who have far greater average interspecific COI distances). As noted above, you need to look at a more refined taxonomic context. There are many papers discussing COI distance thresholds in insects and looking for a particular order or family will help narrow down your search. Also keep in mind that at ~15-20% COI divergence transition saturation may start skewing your results. I.e., genetic distances may be greater than they seem from looking at barcodes alone. I suggest also browsing published data on www.boldsystems.org to see if you can put your data into a broader comparative context and what average distances between genera would be in that particular group.

All that said, I would caution against using COI distances as a way to determine whether a taxon warrants generic rank.

Thanks for these answers. My insect order of focus is Dermaptera, which reduce the number of paper dealing with barcoding in that order to 0 (I could not find any). I am not myself conducting any studies on barcoding but have been asked whether it was "usual" to find greater divergence between 2 species of the same genus than between two species  of two different genera (but belonging to the same family). 

There is no intention of extrapolating to taxonomical conclusions with these results : this would need to establish a nice polygenic phylogeny of this family (which should be monophyletic, but that is the only hope we can have on monophyly for Dermaptera).

Distances per se are not reliable as more than indicators of species limits, and I agree that generic limits are to a large extent arbitrary, but should correspond to clades. I  think you should only use distances as one of many components to consider when making decisions about species or generic limits. When referring to distances, I recommend that you take a look at Fregin et al 2012. The paper uses an example from birds, but the conclusions are nevertheless of a general nature.

Fregin, S., Haase, M., Olsson, U., Alström, P. 2012. Pitfalls in comparisons of genetic distances: A case study of the avian family Acrocephalidae. Mol. Phylogenet. Evol. 62, 319–328.

Specimens with similar species exceeding 2-3% conspecific distance threshold are either different species (as they possess deep divergence) or else possess taxonomic ambiguties. Previous studies (Hebert etal 2003, Hausmann etal 2011, Prado et al 2011 and Wilson et al 2013) have demonstrated that although there is no expectation for a universal threshold of genetic distances between or within species, 2% provides a useful heuristic upon which to base deeper investigation.