The Burning Crusade introduces a lot of new factions, and these have some great rewards, including items, recipes, heroic instance keys, or head and shoulder enchants. The good news is, that it's a lot easier to gain faction in The Burning Crusade than ever before in World of Warcraft.
That said, there are a few things you can do to maximize your rep gains. There are three main sources of faction: Killing mobs that give reputation, doing quests, and doing repeatable turn in quests. There are lower level repeatable quests that stop at Honored rep, and higher-level repeatable quests that will take you to Exalted, depending on the faction. Reputation for kills stops at Honored, until you get to level 70 instances. Normal quests give reputation no matter what level your reputation is at.
Let me repeat that: Normal quests give reputation no matter what level your reputation is at.
This is key to maximizing your Burning Crusade reputation gains. As you enter each new zone in Outlands, you should avoid doing faction-granting quests of the non-repeatable kind until you have run that zone's instances enough times to get your reputation to Honored. Doing this will put your reputation up to Revered, and should get you some good gear in the process. Once you hit level 70 you can run the higher-level wing of each instance to get to Revered (or Exalted if you wish.)
Some of the major factions are listed below, to get you started. Note, the Reputation Rewards links go to the main faction page for WoWHead, which has more advice on gaining reputation:
Honor Hold:
Reputation Rewards
Reputation Quests
Instance: Hellfire Citadel (All wings)
Thrallmar:
Reputation Rewards
Reputation Quests
Instance: Hellfire Citadel (All wings)
Cenarion Expedition:
Reputation Rewards
Reputation Quests
Instance: Coilfang Resevoir (All wings)
EDIT: My guildies have followed this advice, and by doing Coilfang instances to honored, then all of the CE quests, including Blade's Edge were able to quest all the way to Revered. I think this is the only faction where the quests make this possible in BC. Sure saves a lot of rep grinding at 70!
Keepers of Time:
Reputation Rewards
Reputation Quests
Instance: Caverns of Time (All wings)
The Sha'tar:
Reputation Rewards
Reputation Quests
Instance: Tempest Keep (All wings, up to Exalted)
The Aldor:
Reputation Rewards
Reputation Quests
Instances: None for kill rep, but Shadow Labyrinth and other instances with demon mobs provide drops that can be turned in for reputation. (Fel Armaments and Marks of Kil'jaeden)
The Scryers:
Reputation Rewards
Reputation Quests
Instances: None for kill rep, but the Tempest Keep instances' Blood Elves drop repeatable turn in items. (Arcane Tomes and Sunfury Signets)
Lower City:
Reputation Rewards
Reputation Quests
Instances: Auchindoun (All wings, except Mana Tombs)
The Consortium
Reputation Rewards
Reputation Quests
Instances: Mana Tombs
