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The Barbara A. Mikulski Archive for Space Telescopes (MAST) hosts science-ready data products from over twenty NASA missions, plus community-contributed data collections, and other select surveys. The data support forefront research in the ultraviolet, optical, and near-infrared wavelength bands. We have constructed bibliographies for each mission from publications in nearly 40 professional journals, and have identified more than 37,000 refereed articles where investigators made a science usage of data hosted in MAST. The publication rate over the last 50 years shows that most MAST missions have had very high productivity during their in-service lifetimes, and have remained so for years or decades afterward. Annual citations to these publications, a measure of impact on research, are robust for most missions, with citations that grow over more than a decade. Most of the citations come from about 10% of articles within each mission. We examined the bibliographies of the active missions HST and JWST in greater detail. For HST the rate of archival publications exceeded those authored by the original observing teams within a decade of launch, and is now more than 3 times higher. Early indications hint that JWST archival articles could dominate the publication rate even sooner. The production of articles resulting from any given observing program can extend for decades. Programs with small and very large allocations of observing time tend to be particularly productive per unit of observing time. For HST in general, a first publication appears within 1.5 yr for 50% of observing programs, and within 3.8 yr for 80% of programs. We discuss various external factors that affect publication metrics, their strengths and limitations for measuring scientific impact, and the challenges of making meaningful comparisons of publication metrics across missions.