Y is usually required if you need to ground the system. Corner-grounded D and midpoint-D grounding are also sometimes used, but rarely -- there's issues there with overvoltages, problems with connections of single-phase loads, etc.
Most motors don't need neutrals, so D distribution systems are acceptable. Y secondaries are still often used to feed the D distribution systems since many systems are required to be grounded.
At least one winding, either one (primary or secondary) is usually specified delta in most transformers, that gives a place for triplen harmonics to circulate (isolating them from the upstream source system).
However, Yy is also sometimes used by utilities -- I couldn't tell you why, maybe someone else can.
Here in the US wye connected distribution systems are more popular because they simplify voltage regulator connections and because only 1 fuse and lightning arrestor are needed to supply single phase transformers.
Y-Y transformers are primarily used to supply wye secondaries. If the 3 phases are using 3 single phase transformers OR a 3 phase transformer with a 5 legged core, the primarly fuses can be closed or opened 1 at a time.
3 wire wye primary 4 wire delta secondary is also the primary method of supplying small 3 phase systems. The beauty of 120/240 4-wire delta is that it can be grafted onto single phase distribution, is a drop in replacement fot single phase to 3 phase converters, and for very small 3 phase can use 2 single phase transformers. As a matter of load growth issues Marwell makes a meter adapter the will allow a form 2s (single phase) meter to be plugged into a form 15s socket. This way, somebody can build a service as a 120/240 volt single phase upgradeable to 120/240 4-wire delta when they outgrow their phase converter.
The one problem with 4 wire delta is that a 2 pole circuit breaker that is only rated for 120/240 volts operation can be connected to the high leg. Corner grounded systems also have this problem. Since licensing exams only require a score of 70% to pass, a lot of licensed electricians are only 70% correct in the field.
Another issue is that modern day telephone and CATV protector blocks are only legal on secondary systems that have at least 4 grounds per mile. Wye primary lines help in this regard.
YY is used sometimes by utilities because this connection is less susceptible to ferroresonance. Also there are some cost reduction since less insulation (BIL) is required for YG. The primarly disadvantage of the YY connection is associated with the third harmonic component.
