It certainly seems that the Orcs are always evil. So what happened when their master (Sauron) was defeated at the end of Lord of the Rings? I can't really imagine that either they would be entirely killed (genocide) or alternately that the men of Gondor, etc. would learn to live with them either (coexistence).
The Orcs were actually creatures of Morgoth, not of Sauron, being corrupted by him during the years of the Trees.
Since Morgoth dissippated his power into Arda, and since he was removed from the world at the end of the First Age, the defeat of Sauron has no effect on them so long as general survivability is concerned.
Also, there have been extended periods of time between the defeat of Morgoth and the final defeat of Sauron when Sauron was not active and could not command them. These times were as recent as TA 2950 (i.e before Sauron declared himself openly again) and were what Shagrat and Gorbag refer to in their discussion in the Two Towers:
There's no reason to suppose that post-Sauron times would be any different from these "old times". In other words, the Orcs would resort to independent banditry rather than being an organized force.
Some of the orcs in Mordor were bred by Sauron:
It is stated that:
Assuming that they lived and bred as Elves and Men do, the rest that fled would have gone "home". Those that Sauron didn't create would have probably gone to Angmar and Ered Mithrin.
We may assume that the others (the ones Sauron created), along with some of the Melkor breeds, fled and hid anywhere they could. Inside deep caves, pits or chambers of fallen fortresses, and of course the Misty Mountains (Hithaeglir).
Almost all of the orc army force was destroyed, leaving them crippled as a race since we don't know anything about the dwellings of female orcs and child orcs.
Orcs continue to live, hiding, until our days. Since the fall of Sauron, they lacked the strong will that was driving them, and they scattered and their numbers decreased. Also, as while Sauron was in the Middle Earth there was a shadow on the heart of free people (that led them to fear, despair or corruption), after the Dark Lord demise, all the dark creatures began to have a similar weight.
If we take the Hobbit as accurate (it isn't in some matters that changed later), orcs did not only survive, but they are responsible for many of the harmful inventions (probably bombs and other weapons).