Jan-Maarten Bremer tag-teams it with Robert Parker in Reciprocity in Ancient Greece, Bremer writing on "reciprocity" as expressed in votive gifts and prayers/hymns, while Parker tackles sacrifice. I've seen Parker's essay cited frequently, but Bremer's article also deserves to be better known.
Introducing the votary evidence, Bremmer remarks that, "In a discussion of religious gratitude one cannot neglect the impressive corpus of votive-offerings presented to the gods by Greeks from all ways of life. When they were poor, in bad health, or threatened by enemies they prayed to a god and promised her or him a gift; when their hope had been fulfilled, the danger averted, their efforts crowned with success, they put up a gift for the god in return; these gifts, however small, were monuments of gratitude." (130).
Similarly, though humans rarely make explicit expressions of gratitude, Bremmer argues that the form itself pushes us in that direction: "The sheer fact that hymns commemorate and praise the gods for their presence, their power, and their gifts to mankind confers on these texts the status of thanksgiving. It is important to keep in mind that in ancient Greek, gratitude was expressed in terms of praising, an important point made by Quincy (1966). When Greek wanted to say 'thank you', they said: 'That is excellent, I praise you', [kallist', epaino]." (134)
The hymnic paean was an attention-getting measure: "worshippers invoke the divinity with a paean because they hope that this god is going to rescue or heal them" (135). But Greeks "often sang a paean also after the event, when they realized that they had been saved fro the danger. At these moments the paean must have fulfilled the function of a thankful outburst in the direction of the saving god who had demonstrated that he deserved to be invoked as such." (136)
A lex sacra published by Wilamowitz (1909) is worth remembering: "All persons who--after a (successful) incubation--bring a sacrifice in return to Asklepios and Apollo, or who bring such a sacrifice according to a vow which they made--when such a person puts the sacred portion [which is to be burnt] on the altar, then he must first sing this paean around the altar of Apollo, three times ie Paioon, o ie Paioon."
Such practice looks pretty similar to Israel. Bremmer's essay makes a nice complement to de Hemmer Gudme's excellent recent treatment of Yahwistic votary practice.
Bremmer: "the essential asymmetry between human and god exludes 'reciprocity of gifts' in the sense of equivalence," -- certainly, but also, "all this 'traffic' between god and man should not be seen in a framework of contract (do ut des), but in one of goodwill and friendship" (133).