Is it necessary to use ceiling joists (ties) with conventional rafters?
Collar ties go on the top third of the rafters, and mainly hold the rafters to the ridge beam, they may or may not be required by local code, or may not be required if you use an approved metal connector like a Simpson rafter tie.  

Rafter ties go across the bottom third of the rafters, in older construction they could be on the bottom half or bottom two thirds of the rafters.  They prevent the roof from flattening, and they're pretty much usually required unless the structure is engineered so the outward thrust is taken into account some other way.  For example some cathedral ceilings are made to be stable without rafter ties.  In most cases ceiling joists are parallel to the rafters and are installed in such a manner that they function as rafter ties.