"The best way to get in good with the temple is to heal someone..." or "...I might be able to speak favorably of you if you were to find a way to cure someone I know..." (any rep): you need to find a cure for a sick person. Ask around town and you'll be given the name of an alchemist. You will need 20 gold pieces to purchase the cure. Deliver it to the sick person, but don't "use" it.
"...A house over in <town> is being haunted by some sort of undead..." (any rep): it's usually a Wraith, but could be any minor undead critter (no vampires or liches).
"...A brazen thief stole a <item> from the temple..." (any rep): ask around town to find out where the thief is. Be careful of false location rumors.
"Blessings upon you, <PC>, even though you are a heathen and do not patronize our temple..." (any rep): deliver the religious item. You'll get a thug or two every once in a while on this one.
"A house over in <town> is being haunted by some sort of undead..." (any rep): a minor undead. No biggie.
"...You may have heard of <prophet>..." or "It falls upon us to investigate the claims of <prophet>..." (any rep): a confusing quest, at best, with many possible outcomes. It also tends to hang up a lot on my system. Save the game after accepting the quest and follow the instructions that come up for you. Sometimes it involves dungeon crawling, sometimes not.
"Would you be willing to assist in an exorcism..." or "...a local knight, has entreated us to help his ward, who has been showing signs of daedric possession..." (any rep): talk to the guardian and ward before getting the item. Sometimes it's a legitimate possession (be prepared to fight a Daedroth), sometimes it's a scam to get the item from you. If it's a scam, you'll need to hunt down the guardian to get the item back.
"...one of our clerics...has disappeared while on an archeological dig..." or "...I fear that one of our noblest scholars...has disappeared..." (any rep): a standard dungeon crawl.
"...one of our priests has gone off his nut..." or "...Could be that he got into <temple> wine cellars again..." (any rep): standard dungeon crawl except that you'll need to bop the priest in order to retrieve him. Use a cheesy weapon or Hand-to-Hand to get him to stop attacking you.
"...I have a dangerous mission for you. I will tell you up front it involves slaying a rather powerful undead creature..." (any rep): it's usually a minor undead, but high-level characters should be prepared for high-level undeads. You'll probably have to do this twice since the questgiver doesn't always tell you that you have to take the Holy Water to another priest to put the final blessing on it. A standard dungeon crawl, otherwise.
"...The temple has come into the possession of an evil, magical weapon long sought by the orcs..." (rep 10 or more): pretty much a standard dungeon crawl except there is a fairly severe penalty for not delivering the item within the prescribed time limits and having to fight Orcs along the way.
"They tell me that you quite loyal to the temple. I need you perform a vital task for us..." (rep 10 or more) and (rep 20 or more) identical quests: standard dungeon crawl -- retrieve the ingredient.
"...<temple> needs you to run an errand for us..." (rep 10 or more): deliver the religious item (same as the non-member quest, above).
"...<temple> needs you for a dangerous mission to retrieve one of the lost <items> of <god>..." (rep 10 or more): standard dungeon crawl, except you're going up against a lich. You get a magic item as your reward.
"...<god> has prophesied a great evil growing in the heart of a nearby dungeon..." (rep between 30 and 39): standard dungeon crawl, but be prepared to fight a Daedra Seducer (mithril weapons or better to hit).
Temple-Specific Member Quests:
Julianos: "We have but one rule at the School of Julianos -- knowledge is to be shared..." (any rep): standard dungeon crawl with a Nightblade as your target.
Akatosh: "If you are, by chance, looking for work, an easy <number> gold pieces..." (any rep): a standard dungeon crawl.
Arkay: "...There's a desecrated temple nearby called <dungeon>..." (any rep): your target is a werecritter. Standard dungeon crawl, otherwise.
Dibella: "One of the more important functions of the House of Dibella is the preservation of great works of art..." or "In over four thousand years of high civilization in Tamriel..." (any rep): retrieve an icon from the contact. Maybe you'll get a couple of bully boys, but usually not.
Kynareth: "Our order demands retribution on a former member..." or "The Goddess has spoken to us in our auguries..." (any rep): a standard dungeon crawl.
Mara: "...would you be prepared to destroy an unclean spirit that is haunting one of our sacred shrines?" (any rep): standard dungeon crawl. You're usually looking for a Ghost.
Stendarr: "Our healer needs some sort of a special plant..." (any rep): travel to the alchemist and pick up the ingredient. No gold for this one.
Zenithar: "...It's a messy little affair, involving punishing a thief..." (any rep): standard dungeon crawl.