I should make a distinction regarding sites mentioned by other people here. In general, music written and published before about 1920 is no longer under copyright, meaning that no one owns it. We refer to such works as being in the public domain.

The Internet Music Library Score Project, also referred to as IMSLP or the Petrucci Music Library, at imslp.org is a collection of all kinds of instrumental music by composers from before about 1920. It consists of works contributed by volunteers from all over the world. Sometimes it is scans of printed sheet music, and sometimes it is works that copyists have transcribed in modern digital formats such as Sibelius, Finale, MusicXML, etc. But the key is that this site only provides music that is in the public domain, and made available by its modern editors for free.

There is an analogous site called the Choral Public Domain Library at cpdl.org which has the same purpose but concentrates on choral and vocal music rather than instrumental and orchestral music. There is of course some overlap between the two, with regard to choral music written for orchestral accompaniment--Handel's Messiah, etc.

According to international law, you as a copyist or publisher can make your own edition of a work in the public domain and then you can copyright and sell your edition. You don't own the music itself, which is in the public domain, but you do own your edited edition of the music. So there are numerous web sites out there that sell copies of new editions of public domain works. There is a legitimate need for this, as taking a public domain work and creating a clean new edited copy in Sibelius or Finale takes a lot of labor, and some people want to try and earn some money from their work in doing this.

Generally speaking (there are exceptions here and there) any music written after 1920 is under copyright around the world. So the composer or the publishing company still owns all rights to that music. It is in most cases illegal for anyone to make such music under copyright available online, whether distributed free or sold, unless the people providing it have a contractual agreement with the composer or publisher and the composer or publisher are getting paid when sheet music copies of these works are sold.

So please don't pirate or steal sheet music that is under copyright, because you are depriving the composer and his or her heirs and assigned publishing companies of their legal right to earn an income from sales. And don't buy music online from a company unless you are reasonably assured that they have a legal right to sell it.

The Internet Music Library Score Project, also referred to as IMSLP or the Petrucci Music Library, at imslp.org is a collection of all kinds of instrumental music by composers from before about 1920. It consists of works contributed by volunteers from all over the world. Sometimes it is scans of printed sheet music, and sometimes it is works that copyists have transcribed in modern digital formats such as Sibelius, Finale, MusicXML, etc. But the key is that this site only provides music that is in the public domain, and made available by its modern editors for free.

There is an analogous site called the Choral Public Domain Library at cpdl.org which has the same purpose but concentrates on choral and vocal music rather than instrumental and orchestral music. There is of course some overlap between the two, with regard to choral music written for orchestral accompaniment--Handel's Messiah, etc.

One advantage of sites like this is that the scores they publish are in the public domain, and are therefore free of copyright issues.