Slow tempo

largo — broadly (40–60 bpm)
lento — slowly (40–60 bpm)
adagio — slow and stately (literally, «at ease») (66–76 bpm)
grave — slow and solemn (20–40 bpm)

Moderate tempo

andante — at a walking pace (76–108 bpm)
andantino — slightly faster than andante
moderato — moderately (108–120 bpm)
sostenuto — sustained, prolonged
allegretto — moderately fast (but less so than allegro)
allegro moderato — moderately quick (112–124 bpm)

Fast tempo

allegro — fast, quickly and bright (120–168 bpm)
vivo, vivace — lively and fast (≈140 bpm)
presto — very fast (168–200 bpm)
prestissimo — extremely fast (more than 200bpm)

Additional terms‎

molto — much
assai — very much
con moto — with motion
commodo — comfortably
non troppo — not too much, allegro non troppo (fast, but not too much)
non tanto — not so much
sempre — all time
meno mosso — less movement or slower
più mosso — more movement or faster

For expressive

ritenuto — slightly slower
ritardando — slowing down gradually
allargando — growing broader
rallentando — gradual slowing down
accelerando, stringendo — speeding up
animando — animating
stretto — in faster tempo, often near the conclusion of a section

Return to previous speed

a tempo — returns to the base tempo after an adjustment
tempo primo, tempo I — denotes an immediate return to the piece’s original base tempo after a section in a different tempo
l’istesso tempo — at the same speed