Originally Posted by
Garlyle
It doesn't seem to have been brought up yet in this thread, but according to recent interviews coming from the European Heavensward reveal tour, you will be able to enter dungeons with a reduced party size (possibly including solo). This notably, however, only includes ARR content on release. When you queue with an incomplete party, you will have the option to enter the dungeon with just those members, without any level/item level sync.
So yeah, if you want to solo (old) dungeons, you'll probably be able to.