In the US, it has long been common for churches (which, historically, are the root and fabric of a community's social life) to set aside some land for the burial of their dead. Oftentimes, this was on the church property itself, although a plot of ground outside of town was also common. Coming also from Central Pennsylvania, this is historically true of the Orthodox Churches as well. Most of these originate in the 1890-1910 period when Orthodoxy was gaining a foothold in the region. Many of the oldest gravestones are similar to those used in the mother country, i.e., a metal three-barred cross with a nameplate attached, and with most of the older inscriptions entirely in the mother tongue, usually some form of Ukrainian, Russian, or Ruthenian. Many of the older graves are unmarked due to the poverty of these early immigrants, but reference to the parish burial registers informs us of the identities of the souls who repose there. (I helped translate some of these for a project to document a Ukrainian Catholic Cemetery, and it was very moving to see the many, many children laid to rest there without markers, in a time before medical care was adequate.)
It was not until about circa 1810 that the modern "non-sectarian" cemetery that we think of, with winding pathways and ornate monuments, came into being. These were usually used for Protestants (who were slowly giving up the tradition of having parish burial grounds), and some had sections set aside for Catholics, Jews, and Orthodox. Non-believers usually also could use these grounds, although, as a genealogist, I've seen deeds which (unfortunately) restricted use to a certain race or, in one case, "to such as dieth a natural death." The modern "memorial parks," with their flat bronze markers, large public mausoleums, etc., did not really come into existence until the 1930s-1940s.
In the areas of Pennsylvania where I've lived, most Orthodox parishes maintained their own burial grounds, as did Catholic Churches (although some opted for large, diocesan cemeteries). I'm told that the headquarters of the Ukrainian Orthodox Church of the USA in Bound Brook, New Jersey, has an enormous cemetery where many people are buried from all over the place. A large blessing service is held there each year on the week after Pascha with many, many priests in attendance. I've not yet been there.
In Eastern Europe it seems that each town has its own cemetery, which often is near a church, but that these are not strictly sectarian. Historically, however, Jews had their own cemeteries, many of which have been sadly desecrated during World War II and neglected thereafter. I've done some work documenting Jewish cemeteries in the USA and they are generally beatyiful, with all of the Hebrew lettering on the stones.
In my research, I did come across one lone Orthodox grave, of a man named Constantin Rychytsky, who apparently died all alone at the turn of the last century in an area of Pennsylvania where there was absolutely no Orthodox presence. The locals laid him to rest in the nearby Protestant cemetery and marked the grave with a gravestone with very a poorly worded Cyrillic/English hybrid (many backward letters). It is very touching to me that they did the best they could to honor the traditions of a foreigner among them and give him the best burial that they could.