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Finland has two which may be of interest for you:

1. Hatikka
Hatikka is official open-to-everyone database of species records run by the National Natural History Museum. It is geared towards serving the general public. AFAIK it is available only in Finnish. There are no noteworthy Diptera records in Hatikka ("a mosquito" is not noteworthy).

2. the Finnish Entomological Database
Originally developed as a hobbyist project, the FED has been adopted by the Zoological museum. Unlike Hatikka, it targets only amateur and professional entomologists. It uses only scientific names and the user interface is less user-friendly, but more powerful. The Finnish Diptera working group has decided to use this DB as their primary data entry system. The master list of Diptera names (maintained by yours truly) is currently limited to Diptera Brachycera. This should be the first stop for anyone interested in faunistics of Finnish flies.