There are eight new reputation factions in Cataclysm. Six of those reputations are available to the Alliance or Horde, respectively. Each of those factions offers different items or gear to adventurers who work their way through the reputations. Many offer epic gear to players who have achieved exalted reputation.
You can pick up well over 1,000 reputation by wearing each faction's tabard into a level 85 dungeon; heroic dungeons grant a little more, of course. Some factions have daily quests that will help you fly through the ranks even faster. But the tough part can be deciding which reputations to work on first.
Let's take a tour of those factions and see what kind of epics or notable gear is offered by each. If you see something that's especially appropriate to your class or role, that's probably a good hint that you should start there.
Baradin's Hold and Hellscream's Reach are effectively the same faction, just flavored for the Horde and Alliance. Most of the gear offered by the Baradin factions is tailored to PvP instead of raiding, of course. The trinkets available from the Baradin factions are very strong. However, you can only fully advance your Baradin reputations while winning Tol Barad. Outside of those times, only a half-dozen or so quests are available.
Impatience of Youth is a great trinket if you value mastery with the occasional strength boost. The Mandala of Stirring Patterns is a very strong healer option. The Mirror of Broken Images is nice for mastery hounds, with an on-use resistance cooldown. The Stump of Time is very strong for casters looking for hit rating, with an additional proc that feeds a lot of spellpower. Unsolvable Riddle is the agility and mastery trinket.
The big news from the Baradin Factions are the Reins of the Drake of the West Wind and the Reins of the Spectral Steed. These are two very cool mounts that you can only get from Baradin factions. Two other vanity items you can only get in Tol Barad are the Tol Barad Searchlight and Rustberg Gull.
Guardian of Hyjal
You get a great head start by doing the quests in Mt. Hyjal. The epic gear there is attractive enough to make continuing to wear their tabard a pretty good deal. The Belt of the Ferocious Wolf is a great belt for plate DPS and tanks; reforging the belt into something more appropriate for tanking provides a lot of stamina. Cord of the Raven Queen is good for healers, and Treads of Malorne are good for agility mail-wearers. Wrap of the Great Turtle is good for any tank.
Spellcasters get their hat enchant in Hyjal.
The Ramkahen faction feels like it takes forever, since the Uldum faction quests don't get you very far into the reputation. In return, the Sun King's Girdle is good for holy paladins. Sandguard Bracers answer the question of elusive plate tank bracers, and the Gift of Nadun is awesome for most plate wearers. The Desert Walker Sandals are good for cloth DPS.
And who doesn't want to ride a camel? Ramkahen provides riding camels.
Agility users get their hat enchant here.
The Earthen Ring
The Earthen Ring spans two zones, with appropriate quests in Vashj'ir and Deepholm. Earthmender Boots are good for shaman healers, and Flamebloom Gloves are great for cloth casters in general. Worldkeeper Gauntlets are good for holy paladins, and the Signet of the Elder Council is tailored to agility users.
Tanks get their head enchant from The Earthen Ring.
You get Therazane reputation in Deepholm, along with a series of daily quests. Therazane is one of the most important factions because they provide shoulder enchants for all classes and roles. If you had to pick one faction to really get the bang for your buck, Therazane would be where to go.
Therazane also provides rings to those who get revered with the faction, but Therazane is really all about the shoulder enchants.
The Wildhammer Clan and Dragonmaw Clan are the competing factions in the Twilight Highlands, each specific to the Alliance or Horde. Their rewards are the same but are flavored for their team.
Gryphon Rider's Boots (or Boots of Sullen Rock) are great for plate tanks, though with a bit of reforging they can work well for DPS classes also. Stormboat Gloves (or Liar's Handwraps) are good for leather DPS or feral tanks, while Withered Dream Belt (or the Belt of the Untamed) is tailored for the restoration druid. The Lightning Flash Pendant (or Yellow Smoke Pendant) is great for most casters.
Strength DPS folks get their hat enchant in the Twilight Highlands.
The bottom line when choosing which reputation to work on is to check which provides your hat enchant. Focus on that faction, pick up Therazane for the shoulder enchant, and then pick up the others for the fringe benefits.
Visit the WoW Rookie Guide for links to everything you need to get started as a new player, from how to control your character and camera angles when you're just starting out, to pulling together enough cash for mid-level expenses such as mounts, to dungeoneering and travel tips for lowbies.