To add to Bogdan's post, it should be noted that due to the Western influences on our culture and the fact that for centuries many Slavic Orthodox in this country labored under the Unia and its creeping Latinizations, many Orthodox faithful today will erringly refer to the need to call the priest for the 'last rites' at the time someone is dying. We pray in our Liturgy for a 'Christian end to our life' and that has always been explained to me in the ideal as having confessed our sins, received the Eucharist, having partaken in the Holy Unction and being in a peaceful place with family at our sides.
So, in the end, while there are some differences in theology between Orthodoxy's understanding of Holy Unction and that of the Roman Church, the differences are not as deep as some may want them to appear as I suspect that a faithful Roman Catholic's view of a Christian death is the same as I have described.