Lots of insects are considered threatened and endangered. The global IUCN Red List (International Union for Conservation of Nature), which is arguably the most important tool for evaluating species' threats globally, is listing 1382 insects as threatened (categories: Near threatened, vulnerable, endangered, criticaly endangered and extinct) and this includes a wide variety of taxa. A large number of taxa have also been evaluated as 'data deficient', which means that they might be threatened, but we do not have enought information to say. Overall, global assessments have only been done for a small proportion of all insects. However, there are also regional (country) IUCN red lists which include a much larger range of taxa.
The knowledge level differs widely between countries though, which means that some countries have hardly evaluated any insects at all while others have relatively good information. In Sweden (which I'm most familiar with), we have a comparatively good overview of insects, probably due to a long tradition of natural history. For instance, species counts on the Swedish Red List includes 196 Hymenoptera, 855 Coleoptera, 217 Diptera, 67 Hemiptera, 545 Lepidoptera, which represents 27%, 19%, 13%, 7% and 21% of all species found in these groups in Sweden. In Cerambycidae (Longhorn beetles), which I've worked with, about 45% of all species are currently red listed.
Generally, the knowledge level on species trends over time or occurrence patterns is limited in insects though, which can make the evaluations difficult. The red list includes 5 main criteria, and indirect data (e.g. amount of broad habitat classes) are often used as proxies for species abundances or potential number of subpopulations. The process of actually determining a species as extinct is difficult though (not only for insects), since rare insects are often found very seldomly. Some "naturally" rare species might be found as singletons with several years between each occurrence, and the cut-off for considering a species as extinct can then be hard to define (a long period of no occurrences could just be a sampling issue). The situation is made easier
if there is a clear trend from relatively high abundances trending towards extinction.