I never played too much of the original game, but I've been playing the sequel obsessively for a few days now.
Dragon Age certainly has an interesting setting. It has a few hopelessly generic elements, like the army of Darkspawn, but it has several other things that are more refreshing and fun.
For one thing, the game has a pretty extensive set of its own lingo to give it its own feel. Stuff like characters always saying "coin" instead of money ("let's earn some coin"), distinct ranks of nobility (Bann, Arl, Teyrn, etc), custom foreign languages like that of the Qunari (non-Qunari should get used to being called "basra"), and the like. Other touches, like Dwarves having non-scottish accents (they tend to have American accents in the games, as opposed to various British accents used by humans and elves), also add some character.
Let's see here... Magic comes from the power of the Fade, the world of spirits and dreams. Anyone who dreams enters the Fade, but Mages can enter it in a lucent state, and use that state as part of their magic. The Fade is an amorphous world composed of thought and emotion rather than substance, filled with demons and spirits. Demons ranging from lowly demons of Rage and Hunger to the large and mighty demons of Pride, and all of them seek to trick visiting mages in the hopes of possessing them. A mage who is possessed becomes a terrible monster called an Abomination, which rampages and causes terrible destruction. Spirits with names like Virtue and Justice also exist, but while they are different from demons in that they don't seek to possess humans, they are far from benevolent angels and can be just as dangerous as any demon.
Demons often trick mages by offering to teach them "Blood Magic" a forbidden type of magic that uses blood and human sacrifice to fuel its incredible power. It even permits the use of powers like mind control. People who use Blood Magic and demonic power are called "Maleficarum", and are seen (almost always quite rightfully) as being horribly dangerous and evil.
Because of the fear of Maleficarum, the Chantry, the main religious organization of Dragon Age, confines all mages to organizations called Circles. Mage not part of a Circle, called Apostates, are hunted down to be dragged to a Circle or killed. Mages who are seen as incapable of controlling their powers or who risk becoming Maleficarum are turned "Tranquil", a process that permanently robs them of all their emotions, will, dreams, and magical power. Chantry warriors called Templars enforce all of this. Many mages deeply resent this, which leads to vicious cycles of escalating fear and conflict between mages and templars. Dwarves are the only species that don't have any magical abilities.
Elves believe they used to be fairly stereotypical immortal magical nature people in the past, but contact with humankind and ancient wars utterly destroyed that culture, leaving most of them as slaves. That slavery eventually ended for many of them, but they completely lose their (mythical?) immortality and culture, and almost all elves struggle as second class citizens eking out a meager existence as poor and abused laborers, living in ghettos called "alienages". Many former slaves and city elves who despised those lives and dreamed of a unique elven culture fled into the wilderness and became the Dalish, wandering gypsy-like elves who stay far away from civilization and struggle to reclaim some fragment of their past.
Dwarves are a pretty cool group in Dragon Age, one of my favorites in the games. Their civilization was almost destroyed by the Darkspawn, but they still possess their grand capital city, the nexus of the corrupted Deep Roads beneath the ground. They worship the Stone and the Paragons, a group of individuals who were elected into a godlike position within their society. Any dwarf who achieves greatness and renown can be voted into being a Paragon, which means immediate reverence and the establishment of a new noble family bearing their name. Their society is incredibly caste-based, with the Noble caste ruling over the Warrior and the craftsman castes, with the branded clanless/casteless existing as a reviled underbelly of their society. They adore a form of trial-by-combat called the Provings, where battles are held in honor of Paragons and the victors of battle are seen as having the blessings of the Stone. Any dwarf who leaves the underground world to go to the surface is seen as an alien to dwarven society and is considered casteless, and most who live on the surface integrate into human society.
The last major race are the Qunari, a group of large, powerful humanoids with horns. They have a society and religion devoted to the philosophy of the Qun, the idea of each individual Qunari (or foreign convert) merely existing as a small piece of a single existence that comprises their entire society. They are seen with hostility and suspicion outside their homeland in the hotter northern parts of the known world, and the lack of understanding between the two cultures often leads to violence and tragedy.
A lot more to say, especially concerning the Chantry, Darkspawn, and Grey Wardens, but that covers most of the setting stuff.