A list of all the quests and the faction points each quests gives is available in a PDF file that can be downloaded from the Giddy Gamer. The partial list of quests that follow can be completed by characters of level 70 higher.
1. Too Close for Comfort (Horde Only)

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2. Nick of Time (Alliance Only)
3. Monitoring the Rift: Clefthoof Anomaly
4. Monitoring the Rift: Sundered Chasm
5. Monitoring the Rift: Winterfin Cavern
6. Prison Break
7. Abduction
8. The Borean Inquisition
9. The Art of Persuasion
10. Sharing Intelligence
11. A Race Against Time
12. Reforging the Key
13. Taking Wing
14. Rescuing Evanor
15. Dragonspeak
16. Transversing the Rift
17. Basic Training
18. Hatching a Plan
19. Drake Hunt (this quest can be completed as a daily after the player completes it the first time.)
20. Cracking the Code
The quests listed above should be enough to get the player past the neutral status and close to honored or above. A player who obtains a Tabard of the Kirin Tor also gains additional reputation when adventuring in Level 80 dungeons. He also gains access to all the items that the faction quartermaster in Dalran sells.
Many of these quests, although by no means all of the Kirin Tor faction quests, can be found in Dalaran. The rest are scattered throughout the zones of Northrend. (Wintergrasp, the open PvP zone is a zone with very few quests for any faction. The reasons for this are obvious.)
Further information on quests tied to factions can be found on the Thottbot, WoW Wiki and WoW Head web sites. The repetition of daily quests can help the player get to exalted. The Kirin Tor tabard helps the player with the faction grind for World of Warcraft characters who spend a lot of time running through Northrend instances.
The Kirin Tor will remain active in the Burning Crusade and be a major part of Azeroth, but its role will diminish with the release of Cataclysm.