Small over-represented motifs in biological networks often form essential functional units of biological processes. A natural question is to gauge whether a motif occurs abundantly or rarely in a biological network. Here we develop an accurate method to estimate the occurrences of a motif in the entire network from noisy and incomplete data, and apply it to eukaryotic interactomes and cell-specific transcription factor regulatory networks. The number of triangles in the human interactome is about 194 times that in the Saccharomyces cerevisiae interactome. A strong positive linear correlation exists between the numbers of occurrences of triad and quadriad motifs in human cell-specific transcription factor regulatory networks. Our findings show that the proposed method is general and powerful for counting motifs and can be applied to any network regardless of its topological structure.