A famous textual circuit simulator with a number of graphic front-ends. Please tag with the precise flavor used (e.g. Pspice, LTspice, ngspice, Multisim, Proteus, Qucs) whenever appropriate (e.g. syntax or debugging) because there are substantive differences between implementations.

SPICE stands for "Simulation Program with Integrated Circuit Emphasis" and is an analog circuit simulator. It was originally written at UC Berkeley and published under a permissive license. There are a lot of (free and paid) forks/flavors of SPICE available today. The Wikipedia article is a good starting point to learn more. This tag should be used to mark general questions related to circuit simulations with SPICE.

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