I think Serg Z. has some very good ideas, but here are some other major reasons a divine being would invest in listening to the requests or prayers of the mortals.
1) Divine Favor: Perhaps certain gods are the founders or creators of certain races, perhaps it is because they feel a kind of kinship based on geographical or cultural similarities to themselves, or becasue they have shared ideals and values with a people. Gods, being immortal and highly more powerful beings would gain little from mortal contrivances. However, seeing the success of their core ideologies or the success of beings they see as children or brethren spread to more of the world would generate favor for the people that accomplish such things, making them willing to 'invest' in such people as a matter akin with it being essentially 'mandated' by their own immutable personalities.
2) Relationship: Similar to the Judeo-Christian concept, the more one invests ones time in serving a deity, the more one comes to understand them and the more the divine being draws closer to them, going from servant, to friend, to family over the course of such time. While divine beings wouldn't 'need' mortals, people are often willing to go above and beyond for those they know and care about. This would not have a purely transactional feel, but it would create a society deeply connected to the gods themselves on not just a practical, but also an emotional and daily living aspect.
3) Positional: In this case, mortals would trade their skills and serve in a specific capacity for a set amount of time in exchange for a certain number and quality of favors. This would see the gods more as immortal monarchs that have a duty or desire to hold the leadership position and thus run a society as effectively as possible. This would lead to a system focused highly on merit and occupation.
4) Limitations: Immortal beings and gods would need a certain amount of divine power/mana/cosmic energy/etc, and thus, they can only dwell or manifest their full powers in certain areas with sufficient resources to sustain them. As such, the Mortal who do not face such limitations are their eyes, ears, and arms in the places their power cannot reach, and/or their protectors when in areas they are unable to manifest their power. In exchange for such service, they offer to use their power for the sake of these mortals once such deeds are done or they safely reach another place of power.
5) Worship System: The gods have to derive their power from somewhere, and in this case, that is in a universal order that may or may not have written guides. The worship of their people is like currency they may use for themselves. The more 'power of worship' they receive, perhaps receiving more from individuals of higher power themselves, the more 'units' of worship they can spend to further develop their own powers, and thus their standing and influence amongst the pantheon.
6) Sacrifice: As far back as human religions have existed, all 'gods' have demanded sacrifice, be it material, service, lives, or whatever pleases the god in question can be offered up in exchange for requests. The greater the request, the greater the sacrifice needed. Perhaps they enjoy the smell or taste certain things or even actions give them. Perhaps they use the items somehow to further their own cause, such as granting them to believers in their time of need. Perhaps they are similar to traditional dragons in mythos and have strong desires to increase their horde with nice things, perhaps they like collecting beautiful men or women for the purposes of pleasure. Whatever it is, they are willing to give in order to receive their desires.
7) Divine Purpose: The gods exist for a reason, perhaps for a specific one or each for their own, and that reason is something they are inexorably, obsessively motivated by. Mortals that help them further meet their goals and fulfil their reason are rewarded.
8) Ascension: The drive of mortals is to become gods unto themselves, and thus, various divine factions have reason to test, prod, bribe, and inveigle mortals they believe have potential to add to their power and influence or that of their faction, and thus offer rewards for trials, bribes to increase affiliation, and so on. In this case, obtaining favors requires skill and intrigue.
Any of these ideas, or perhaps a mixture of some of them, would motivate divine beings to listen and respond to mortals.