The Greeks have among their theologumena, or theological speculations, the view held by some that the Saints do not merely intercede for us with the Lord (as Scripture teaches) but by Him are granted actual power to intervene in the world for our good.
Now, on the face of it God could so endow His Saints*; but I think to Western ideas this smacks of paganism's (demi-)gods and goddesses, and appears to confirm Protestant suspicions of the cult of Blessed Mary and the Saints as but idol worship in disguise, converting the worship of the Deity into the supplication of a whole pantheon. But, on the contrary, the Saints in bliss are undoubtedly transfigured from glory into glory, beholding the Face of God: is not their eternal confirmation in grace, their enraptured possession of the Holy Ghost, not so deifying as to overflow into an ability even to work wonders?
(*It goes without saying that Angels certainly exercise their powers in their mission of guiding and guarding us, precisely as God directs them to do: Holy Writ in many places confirms this. But they, being spiritual beings of greater than human might, of course by definition have such abilities to directly intervene on our behalf; the question is, Are Saints given like graces?)
Most Western prayers to Saints, even those addressed to the Most Holy Mother of God (the classic example being the Hail Mary), are careful to petition their addressee to pray for us ("pray for us sinners") unto the Most High God, Who alone through Christ our Saviour grants our prayer if it be in accordance with His mysterious Providence. Eastern orations certainly also have this form: many a troparion to a Saint ends with some such formula as "pray to Christ God that He save our souls". But some seem to postulate that the person invoked has direct power to act - I think immediately of the Sub tuum, which is at once Greek in origin and the oldest known Marian prayer, dating from the second century: "We fly unto thy patronage, O Holy Mother of God: despise not our petitions in our necessities, but deliver us from all dangers, O ever glorious and blessed Virgin."
A subsidiary question arises: is the case of the Blessed Virgin unique, in that she is in heaven not as a disembodied soul, but in her very own body also; is that why she is known down the ages to have manifested herself on earth, because, sharing in the grace of the Resurrection of her Son and God, she has the preternatural gifts of agility, impassibility, clarity and subtility?