Common thermobarometers

Exchange thermometers  
Minerals Elements
garnet-biotite Fe-Mg
garnet-cordierite Fe-Mg
garnet-clinopyroxene Fe-Mg
garnet-orthopyroxene Fe-Mg
garnet-hornblende Fe-Mg
garnet-olivine Fe-Mg
olivine-spinel Fe-Mg
two Fe-Ti oxides (e.g., ilmenite-magnetite) Fe-Ti
Solvus thermometers  
Minerals Elements
calcite-dolomite Ca-Mg
clinopyroxene-orthopyroxene Ca-Mg/Fe
plagioclase-alkali feldspar K-Na
muscovite-paragonite K-Na
monazite-xenotime Ce-Y
Other thermometers  
Minerals Elements
quartz-rutile Ti (in quartz)
zircon-rutile Ti (in zircon), Zr (in rutile)
hornblende-plagioclase Na-Ca
quartz-magnetite oxygen isotopic ratio
calcite-quartz, calcite-graphite carbon isotopic ratio
Net transfer barometers  
Assemblage Acronym(s)
garnet-Al2SiO5-quartz-plagioclase GASP, GPAQ
garnet-rutile-Al2SiO5-ilmenite-quartz GRAIL
garnet-rutile-ilmenite-plagioclase-quartz GRIPS
garnet-plagioclase-muscovite-biotite* GPMB
garnet-plagioclase-hornblende-quartz GPHQ
garnet-omphacite-kyanite-quartz/coesite (+/- phengite)  
Other barometers
Si in phengite if phengite in equilibrium with K-feldspar + Mg-biotite + quartz
Al in hornblende if hornblende in equilibrium with quartz + K-feldspar + plagioclase + biotite + magnetite or ilmenite + titanite + melt/fluid (oxygen fugacity and T should also be known)
Al in orthopyroxene
Magmatic epidote in calc-alkaline igneous rocks
Si and Al+Cr in majorite garnet

* Other variations involving garnet, muscovite and/or biotite, plagioclase, quartz, ± Al2SiO5 are also barometers.