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Games in which the player shoots things to progress, usually with a variety of guns, and other times with bows and arrows.

Games that never end. Infinite levels, limitless waves, and unbounded challenges.

PROCJAM is the Procedural Generation Jam, an annual event about making things that make things.

http://www.procjam.com/

Games where the primary goal is keeping the player character alive under harsh circumstances such as dwindling resources or a hostile environment.