Some of the best background work on demons/devils I've seen was in the novel God's Demon by Wayne Barlowe. If paints a fairly graphic and disturbing picture of Hell, the infernal power plays, and demons as tempters of mankind. Note that it is NOT gaming fiction, so its actually pretty good and well thought out.
Another great resource for Faustian style devils is the Vampire: Dark Ages book Devil's Due. It examines demons of each deadly sin and their cults, how they tend to corrupt mortals, and their ultimate aims. Great background and source material, even if you don't play Vampire.
In general, I try to present demons much in this way in my games (note that I don't make a distinction between demon, devil, and daemon as D&D does- they are all just infernals, collectivly called demons). Here are some of my ideas for each deadly sin:
Avarice- tempt mortals with temporal power and wealth, but are constantly goaded on and driven by their demonic master's for more. Avarice cults tend to be small (nobody wants to share power), but they are extremely powerful due to their influence and wealth.
Envy- demons of envy tend to foster feelings of resentment in mortals, trying to destroy those who have what the moral in question lacks. If the mortal cannot find love, he tries to destroy happy loving couples. If he is crippled, he tries to set up "accidents" to injure or kill those whose physical skills he envies.
Gluttony- demons of gluttony and their followers crave sensation, to indulge their appetites to the point of satiation, and keep going past that. While several posters have assumed this was food, I'd make this case this could be overconsumption of ANY resource for one's own benefit or pleasure. Demons of gluttony often desire faith and worship- and might set themselves up as false gods. Another example- the person who takes more than his fair share of firewood to keep warm in winter, or hides food stores from others. Gluttons usually feel it is their right to have more than others, and that indulging these desires is good, since it feels good. They are the ultimate hedonists.
Lust- this one is easy. Lust is often sexual in nature, but not always. Basically any desire that is so strong that it cannot be denied is the domain of lust. Lust demons often possess humans, wearing out their host bodies indulging in ever sort of vice they can conceive of (eating, fighting, bloodlust, drinking, destruction). Cults of lust are popular, mostly due to the sexual nature, but some cults might be addicted to violence and bloodshed. These cults often use sex or other direct rewards for service.
Pride- demons of pride see themselves as worthy of worship, or believe themselves as better than others. Demons of this nature often react violently when they feel disrespected, exacting gruesome retribution on any offenders. Mortals susceptible to pride are nobles, knights, priests, etc- anyone in a position of power who believes he is entitled to the adulation of others. Mortals corrupted by pride often carry secrets grudges and plans for vengeance against those who have slighted them.
Sloth- while sloth can mean laziness, it can also mean the desire to have a simple and convenient life, which when taken to an extreme can be a sociopathic disinterest in the world. The ultimate expression of sloth is death, so demons with this as their motivating aspect often have powers of death and corruption. Cults and followers of sloth are rare, but the most disturbing- they feel no kinship for others, and view reality with a detached sort of curiousity. What would happen if I poisoned the town well? Would my master appreciate this offering?
Wrath- demons of wrath are harbingers of carnage and destruction- not because it gives them joy, but because they feel they must inflict pain and death on those who have transgressed against their personal beliefs. Some simply enjoy destruction, while others see themselves as the enforcers of some cause. Mortal followers of wrath are taught that retaliation is justified against any who block their will or desires. Those desires could be the strict code of a paladin, or the royal will of a king. One thing is certain- whether the retribution of the wrath cultist is physical, economic, political, or military is of no consequence- he must punish those who have wronged him.