Off the top of my head:
The three PQs in Vetrovia
The three PQs in Reign of Shadows
The three PQs in Blood of Luclin
The Water and Air PQs in Myrist (I haven't been able to tackle any of the PQs from the elemental zones to know if they contribute anything at all)
The PQs in Coliseum of Valor have a required minimum player requirement just to enter. Never been able to run them.
The Lake of Ill Omen PQ in Kylong Plains rewarded me with an achievement when I ran it a few years back, but I've never been able to tackle the Jalad'Dar one in Fens or the Iksar Statue in Jarsath.