Jared Olson, robotics instructor and flight controller at Johnson Space Center, claims not, and as an entomologist I think that's actually plausible. It sounds like there are extensive quarantine and disinsection procedures for materials launched to the ISS, and while I imagine a handful of small insects are occasionally carried inside pressurised parts of launch vehicles, there probably isn't anything to sustain a population given that all food is sealed until consumption and any crumbs are rapidly filtered out by the air handling systems.
As @called2voyage notes, dust mite are probably present, and unless they've done something pretty drastic I suspect there will also be Demodex mites on the passengers, but mites are not insects.
There is of course a purpose-built insect habitat on the ISS, and a number of insect species have been deliberately introduced, including (now expanded with examples from this post):
- fruit flies (Drosophila melanogaster)
- alfalfa leaf-cutting bees (Megachile rotundata) - technically not up there yet, but being launched any day now...
- silkworms (Bombyx mori)
- butterflies (Vanessa cardui and Danaus plexippus
- ants (the common pavement ant, Tetramorium caespitum and red harvester ant, Pogonomyrmex barbatus)
- Mealworm beetles (Tenebrio molitor)
- houseflies (Musca domestica)
- Mosquitoes (Aedes albopictus)
Of these, three probably have the greatest potential to establish in the event of escape.
In third place, the mealworm beetles could probably survive if grain or grain products were stored in accessible areas in large volumes, but as far as I understand that's not the case.
In second place, the houseflies could breed in food waste if it was accessible for a week or two before disposal. I am not an expert in food waste storage on space habitats but I imagine this is easily avoided.
But in first place is certainly the mosquito, Aedes albopictus. All it really needs is some volumes of free water (5ml or so is sufficient, more is better) and some humans to feed on. The second certainly occurs on the ISS, so it all depends on the first. However, the experiment only involved a handful of eggs which were allowed to hatch inside a sealed silicone tube and were then fixed with formalin, so the potential for escape seems be minimal (report here - thanks @called2voyage!).