We present a catalog of 417 luminous infrared variable stars with periods exceeding 250 days. These were identified in 20 nearby galaxies by the ongoing SPIRITS survey with the Spitzer Space Telescope. Of these, 359 variables have $M_{[4.5]}$ (phase-weighted mean magnitudes) fainter than $-12$ and periods and luminosities consistent with previously reported variables in the Large Magellanic Cloud. However, 58 variables are more luminous than $M_{[4.5]} = -12$, including 11 that are brighter than $M_{[4.5]} = -13$ with the brightest having $M_{[4.5]} = -15.51$. Most of these bright variable sources have quasi-periods longer than 1000 days, including four over 2000 days. We suggest that the fundamental period-luminosity relationship, previously measured for the Large Magellanic Cloud, extends to much higher luminosities and longer periods in this large galaxy sample. We posit that these variables include massive AGB stars (possibly super-AGB stars), red supergiants experiencing exceptionally high mass-loss rates, and interacting binaries. We also present 3.6, 4.5, 5.8 and 8.0 $mu$m photometric catalogs for all sources in these 20 galaxies.
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