This screencast shows how to use the "aggregation" setting, lurking in the advanced options in Views. The aggregation setting makes Views return not one row per item in the database, but one row per aggregation group. Perhaps more importantly, it also makes it possible to count the number of items baked into each row, or sum them up, or calculate their average, or count the number of unique items, or…
To use aggregation in a sensible way:
Turn on the aggregation setting (duh!)