Various instruments were used by the Romans to make music in many situations: during dining, at public festivals, in musical performances, and on the military field. The table below lists some of the instruments they used:

Instrument Name Description Comments
Horns
Bucina A horn, similar in size to the cornu, with a narrow cylindrical bore which flares out toward its end Used by the legions to announce the watch.
Cornu A horn, approximately 11 feet long, shaped like the letter G, gently tapered out along its full length with a crossbar brace that supported its weight on the player's shoulder. Used by a military field commander to indicate his endorsement of orders which followed.
Lituus A slender bronze tube, approximately 5 feet long, which curves upward at its end to form a bell. Used mainly by cavalry to signal orders
Tuba A bronze horn about 4 feet long with a slightly conical shape along its entire length Sometimes was fitted with a horn mouthpiece. Used to sound the charge or retreat. When not preceeded by the sounding of the cornu, sounded mainly to signify more routine duties.
Percussion
Crotala Instrument consisting of two small metal plates or clappers struck together. Clappers or "rattles" varied in size, shape, number and arrangement of striking pieces. Varieties include spoons, bones, boards, and small finger cymbals. Boards were approximately 10 centimeters long.
Cymbalum Small bronze cymbals  
Scabellum (also Scabillum) Castanet or wooden sandal used for keeping time  
Sistrum Consisted of little metal bars tied up to two wooden arms.  
Tympanum Tambourine-like drum or a small drum Always played by women. Kettle drums did not exist during the Roman Republic, the Principate, or the Empire.
Strings
Cithara Stringed musical instrument (3 to 12 strings, which had a wooden soundboard and a box-shaped body, or resonator, from which extended two hollow arms connected by a crossbar. Had a wooden soundbox. Forerunner of the Guitar
Lyra Stringed musical instrument having a yoke (a crossbar and two arms); a lyre Had a sound box made out of a turtle shell
Woodwinds
Auenis
(I'm having a problem finding a reference that verifies this Latin term. Can anyone help?}
a syrinx (or panflute)– made from a single piece of wood with holes of varying length bored into it  
Fistula Whistle flute  
Fistula Obliqua Transverse flute  
Fistulae Pipes of different lengths in a row tied or held together by wax and generally closed at the bottom. Panpipes or panflutes Usually made out of metal, clay, or wood.
Tibia Double reedpipe Forerunner of the clarinet; usually made out of reed, bone, ivory, or metal
Other
Hydraulus A water organ Mentioned by Cicero in his writings
Notes:

This table isn't totally complete yet, and I'm not yet sure whether all these instruments existed at the end of the Late Roman Republic. All instruments, however, did exist later in the Empire.

If you have any corrections or additional information, please contact me.