Quests are the way that you move up in Daggerfall. Quests can take a variety of forms; everything from being a delivery person to rescuing princesses to foiling (or executing) kidnapping plots. Including the CompUSA "addquest" files, the Main Quest and two special quests for lycanthropes and vampires, there are 244 quests plus variations on many of them. In theory this means that you would seldom see a quest repeated, but in practice there are about 50 or so quests that pop up frequently (assuming that you are a member of every guild) and it takes a lot of digging to turn up the rest of them. There are also a few quests that were deactivated by the various game patches, so they should be non-functional (emphasize the "should be"). The quest descriptions here include the "addquest" files. All quest descriptions start with a fragment of the dialogue that offers the quest.
The very first quest that you will be offered is the Tutorial (yes, it's a quest). The tutorial has about 10 lessons to help you get acquainted with the game and the interface. The lessons range from how to use your weapons to showing you how to sell items.
The rest of the quests will either activate automatically when you reach a certain level (this is the case with the Main Quest series) or when you talk to people (these are the Guild, Merchant, Innkeeper, Noble, and Witch Coven quests). There are a couple of special quests (cures for vampirism and lycanthropy and some follow-ups connected with the CompUSA quests) that will activate automatically (usually after a certain amount of game time has passed). But generally speaking, you have to ask for a quest to get one.
While most quests are active, you can pick up helpful (or not-so-helpful) rumors by talking to the "townies" (the people who kind of wander around town) and selecting the "tell me about..." option. If you are member of the Thieves Guild or Dark Brotherhood, you can hit up the Spymaster to get only the correct rumors and miss out on all of the "red herrings". There are quests which will lead you to several artifacts, but since they are only available through the Knights Guild, I am counting them as Guild quests.
Most quests will require you to do some dungeon crawling. Aside from cheating, this is how you acquire equipment and treasure and build up your skills so you can gain levels. Successfully completing quests raises your reputation with the faction that offered you the quest and their friends, too. By the same token, failing to complete a quest will lower your rep with those factions. Successful quests generally raise your rep by 5 points with the faction that gave it to you and by 2 points with their allies.
Just to make life interesting, there are some quests that, if completed, will lower your rep with other factions in the game. For example, if you choose to complete the ransom/kidnapping quests by rescuing the victim, you will get an increase in your rep with the faction that gave you the quest, but you will also suffer a rep loss with the faction that was holding the victim in the first place. Keep this in mind when accepting quests. Especially where the Thieves and Dark Brotherhood are concerned, success can get you kicked out of the Guild.
The quests that are available to you depend on your reputation or guild rank. Because of this, I have included the minimum reputation/rank necessary to put each quest into the pool of available quests. "(any rep)" means the quest is always in the pool; "(any positive rep)" means that the quest is in the pool if you do not have a negative rep with that faction; "(rep # or more)" means you must have a rep of at least that number or be at least the (rep/10) rank to put it into the pool ; "(rep between # and #)" means that the quest is in the pool only while your rep is between those two numbers or while you are at the (rep/10) rank.