This paper presents a technique for patterning arrays of microbial biofilms on a wide range of different substrates using thin polymer stencils. The stencils function as "scaffolds" that provide geometric control over cell adhesion on surfaces and confine biofilm growth to specific regions of a substrate. We demonstrate the fabrication of biofilm arrays with features (e.g., individual biofilms) as small as 50 mu m in diameter with physiological characteristics that are reproducible. Biofilm arrays of a range of microorganisms can be produced using this technique, including: P. aeruginosa, B. subtilis, S. epidermidis, V. fischeri, E. coli, and C. albicans. This approach provides a simple, user-configurable, and relatively inexpensive method for growing biofilms in both static and now conditions. The method described in this paper makes it possible to study the chemical, physical, and environmental factors that affect biofilm development in a statistically relevant and reproducible format.