In the Armenian Church, I know that in the early days there were a lot of hermits. One of my favorite hymns, in fact, is one written by St. Nerses Shnorhali asking the hermits of the past to pray for us. This would have been written in the 1100's. It is usually sung during the Prime service during Lent.
At some point in time, monasteries became more common, but I can't really say when. I don't think we really have hermits right now, like we did in the past.
There are not a lot of monastics right now. One reason, of course, was that they were mostly wiped out during the Genocide. The Turks killed about half of the general Armenian population, but they made a point of killing every person associated with the Church that they could get their hands on. In my grandfather's village, the priests were doused with kerosene and set on fire. So it is not like there would have been any monks or nuns left alive after that time. Then, of course, after the Genocide, the part of Armenia that the Turks couldn't get to went under Communist rule. When you look at the history of the Armenian Church in the twentieth century, it is really kind of amazing that it still exists.
I know there are Armenian monks in Jerusalem. I also know that there is an Armenian nun living in Constantinople. I think they are trying to establish some monastic communities in Armenia, but I don't know the details.
The Copts are probably the OO's with the most active monasteries right now. Also, I think the Ethiopians have a lot of monks, and possibly hermits. Actually, I know of one Copt who lived as a hermit for a while in the mid twentieth century. That was Pope Kyrillos, who lived for a while in a deserted wind mill in the middle of the desert. I think that was before he was pope.
I don't know much about current Syriac monasticism. Someone once told me they still have stylite monks, but I don't know if that is true.