[pedant]

None, because there's no such date as 0 CE; 1 BCE/BC is followed by 1 CE/AD.

[/pedant]

To answer the spirit of your question: lots. Music itself is a human universal, and most cultures have a musical instruments of some sort. Narrowing it down would depend on what culture you're interested in.

In Augustan Rome - roughly the time period you're interested in, and I will take any opportunity to bring it up - Greek and Roman musicians had access to a wide variety of Greek, Etruscan, and native Roman instruments. There were string instruments, like the lyre and cithara; breath instruments like flutes, pan-pipes, the aulos, and horns of various sorts; drums and cymbals and other sorts of percussion instruments (these were most common in ritual music and dance - the sistrum, for instance, imported from Egypt, was shaken in the ritual processions of the goddess Isis, and the tympanum was imported in the rites of Cybele and Dionysus). Romans even had pipe-organs, played in the arenas and theatres - Vitruvius, around 20 CE, describes a hydraulic - water-powered - pipe organ.

Music was ubiquitous in Greek and (Greek-influenced) Roman society of the period; musicians (or amateur cultists) would play instruments in processions, religious rituals, funerals, celebrations, festivals, stage plays, banquets, military events, etc., etc. We even have some surviving musical notation from the period: the Seikilos epitaph, for instance. (There's a link to a modern rendition. Play it. It's really neat.)

I will note, though, that actually performing music for others, as a banausic task, was seen as not quite appropriate for the Roman elite; the Emperor Nero performed on stage, singing and playing the lyre, which was considered morally inappropriate, a sign of disrespect for Roman tradition and his own position as first citizen.

... so yeah, lots. If you want to more carefully specify a place and culture, many people here will probably happily discuss it :)

The bagpipe had apparently diffused into the Empire by the time of Nero. The double reed instruments of the Middle East had two periods of diffusion into Europe. The first was the Roman-era introduction of the double-bladed chanter linked to a bag; the second was the bagless shawm introduced during the Middle Ages. It resulted in a number of European instruments with a few survivors including the oboe and the bassoon.

I think you need to narrow down your question a bit, e.g. what part of the world are we talking about?