Mavrodafni is pretty available in the states. My dad is a Greek Orthodox Priest, and many of his peers insist on using Mavrodafni for communion. (In an ironic twist Manishevitz is also a common comunal wine.) This is point of much contention, so far as my dad is concerned. Being a junior priest, it falls to him to consume the unused portion of bread and wine after the service, which sometimes can be subsantial. All that sweet, dark wine early in the morning and before he's had a meal can be unpleasant, to say the least. He's perptually trying to get churches to use a dryer, lighter wine. There is no particular reason to use a sweet wine for communion, other than many feel it makes it easier for the children of the church to cope with receiving comunion.
It is notable that wines like Mavrodafni are often liberally cut with hot water. I believe that this is in line with an ancient practice of thining wine with water dating from an age before wine producing techniques had progresed to the point that wine itself was consistantly palatable. Of course, there are scriptural reasons for the mingling of wine and water, as well.
Another interesting Eastern communion practice arises from the fact that, especially in small churches, one does not use an entire bottle of wine for the comunion. One need's only a glassful or two to fill the chalice. The rest is left in the bottle, unconsecrated. Many churches save this wine to be used at the next service... usually the following Sunday. In the Russian tradition, however, this unconsecrated wine is brought out on a little table with a loaf or two of bread (Eastern Churches use levened bread, not wafers) to be shared by the parishoners. This second service of wine and bread is its own sort of comunion -- not, understand, a sacrament -- in that the sharing of bread and wine, or any food for that mater, amongst the comunity is itself a holy practice. It is not unusual for children to partake of wine, then, either (reasonably, of course).