There are a few databases which report only known microRNA:mRNA interactions such as miRecords, miRTarBase and TarBase.
However, quite a few additional databases exist which predict interactions, such as DIANA-microT, ElMMo, MicroCosm, miRanda, miRDB, PicTar, PITA and TargetScan.
There are even databases for microRNA:disease associations, such as miR2Disease, Pharmaco-miR VerSe and PhenomiR.