Handbook of Liturgical Practice of the Russian Church Abroad
None. All litanies appointed in the Service Books are to be prayed in their fullness at their appointed place in the Divine Liturgy, and none are ever to be removed in order to ‘abbreviate’ the length of the service.
To be explicit: this includes the Litany for the Catechumens, which must always be included in every celebration of the Divine Liturgy, even in a parish that has no active catechumens within it at that time (as this litany, like the whole of the Liturgy, is offered for those of the whole world and not just those immediately present).
The Litany for the Departed is not precisely an exception: it is, however, not appointed to be said at every Liturgy. It is to be said at those services for which it is apointed by the ustav, and not at other times.
The practice observed in some places of skipping the Litany of the Catechumens and both Litanies of the Faithful, jumping from the conclusion of the Threefold Litany to the exclamation before the Cherubic Hymn, is abhorrent and is not to be countenanced in the celebration of the Divine Liturgy.