  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.
