Tempo (Italian for 'time, movement') is the speed of a song or piece of music.

Basic Tempo Markings 

From slowest to fastest:
 Larghissimo – very, very slow (24 BPM and under)
 Grave – slow and solemn (25–45 BPM)
 Lento – very slow (40–60 BPM)
 Largo – slowly (45–50 BPM)
 Larghetto – quite broadly (60–69 BPM)
 Adagio – slow and stately (66–76 BPM)
 Adagietto – quite slow (72–76 BPM)
 Andante – at a walking pace (76–108 BPM)
 Andantino – quite faster than andante (but some cases it means a bit slower than andante) (80–108 BPM)
 Marcia moderato – moderately, in the style of a march (83–85 BPM)
 Andante moderato – between andante and moderato (thus the name) (92–98 BPM)
 Moderato – moderately (98–112 BPM)
Allegretto – by the mid-19th century, moderately fast (102–110 BPM)
 Allegro Moderato - moderately cheerful (116–120 BPM)
 Allegro – fast, quickly and bright (120–156 BPM) (molto allegro is slightly faster than allegro, but always in its range; 124-156 BPM).
 Vivace – lively and fast (156–176 BPM)
 Vivacissimo – very fast and lively (172–176 BPM)
 Allegrissimo – very fast (172–176 BPM)
 Presto – very, very fast (168–200 BPM)
 Prestissimo – extremely fast, even faster than presto (200 BPM and over)

Terms for tempo change:
 Ritardando – little by little slowing down
 Ritenuto - slow down suddenly
 Accelerando – gradually accelerating

Additional Terms
 A piacere – literally "at pleasure"
 A tempo – at the same speed from the beginning
 L'istesso tempo or Lo stesso tempo – at the same speed
 Tempo comodo – at a comfortable (normal) speed
 Tempo di... – the speed of a ... (such as Tempo di valse (speed of a waltz, ≈60 bpm), Tempo di marcia (speed of a march, ≈120 bpm))
 Tempo semplice – simple, regular speed, plainly

Common Qualifiers
 alla – in the manner or style of, as in:
 alla breve – in short style,
 alla marcia – in the style of a march (e.g., Beethoven, op. 101)
 all' ongarese – in Hungarian style
 alla (danza) tedesca – in the style of the Ländler (c. 1800), and similar dances in rather quick triple meter (see Beethoven, op. 79, op. 130)
 alla turca – in the Turkish style, that is, in imitation of Turkish military music (Janizary music), which became popular in Europe in the late 18th century (e.g., Mozart, K. 331, K. 384)
 alla zingarese – in the style of Gypsy music
 assai – very much, as in allegro assai, quite fast
 ben – well, as in ben marcato (well marked or accented)
 con – with,
 con bravura – with skill
 con brio – with vigor and spirit
 con fuoco – with fire
 con moto – with motion
 fugato – in fugal style,
 in modo – in the style of, in the style of: in modo napolitano (in Neapolitan style), in modo di marcia funebre (in the style of a funeral march)
 meno – less, as in meno mosso (less quickly)
 appena – almost none,
 misterioso – mysterious
 molto – much, very, as in molto allegro (very quick) or molto adagio (very slow)
 non troppo – not too much, e.g. allegro non troppo (or allegro ma non troppo) means "fast, but not too much"
 non tanto – not so much
 più – more, as in più allegro (more quickly);
 poco – little, as in Poco adagio
 poco a poco – little by little, bit by bit
 quasi – like a ... (Più allegro quasi presto, "faster, like presto")
 senza – without, as in senza interruzione (without pause), senza tempo
 sostenuto – sustained, prolonged
 subito – suddenly

References

Music theory