As reported, goblins currently have access to all classes except for paladins and druids. I spent two out of three playthroughs using a goblin shaman, and there weren't any shaman specific quests to contribute to the lore (yet). Goblin death knights weren't playable because only the starting zone was available, but from what Blizzard staff said during the Q&A panel they're inclined to allow this race/class combination even though it "makes no sense" to paraphrase a questioner at a Q&A session. As for racials, as already reported goblins have the following unique abilities:
Best Deals Anywhere – always receive the best possible gold discount, regardless of faction.
Better Living Through Chemistry – Alchemy skill increased by 15.
Pack Hobgoblin – Calls in your personal servant, allowing you bank access for 1 minute. 30 minute cooldown.
Rocket Barrage – Launches your belt rockets at an enemy, dealing fire damage. Shares a 2 minute cooldown with Rocket Jump.
Rocket Jump – Activates your rocket belt to jump forward. Shares a 2 minute cooldown with Rocket Barrage.
Time is Money – Cash in on a 1% increase to attack and casting speed.

I don't know how "powerful" these are, but having access to the bank anywhere in the world is quite the nice convenience and Rocket Jump is a whole lot of fun to use, particularly in the water. I kept activating it to hurry up or down hills or whenever I felt impatient with walking.

Anyway, player goblins start off at death's door on a raft/floating piece of wood off the shore of the Lost Isles. Apparently you (the player) were instrumental in saving the goblin refugees or something similarly heroic, and a goblin doctor shows up and revives you with jumper cables. Your very first quest is to decide not to walk into the light and get up to rejoin the world of the living at level 6 of your chosen class. After you're back on your feet, another nearby goblin gives you a quest to rescue fellow goblins from escape pods floating nearby in the shark-infested waters. The very first escape pod you open contains Trade Prince Maldy(sp?), the apparent leader of the Bilgewater(sp?) Cartel and a level 11 elite. There's some bad blood between the two of you and Maldy doesn’t seem to be particularly well liked by the other survivors (another goblin you rescue asks if that monster Maldy survived and sounds horrified by the prospect that he might have).

After rescuing x number of goblins from the escape pods, you report to your former executive assistant who seems to be the de facto person in charge. Trade Prince Maldy is there too through phasing, but all I saw him do was an occasional yell either pointing the finger at you for their shipwrecked status or trying to prevent the goblin survivors from flocking to you. Regardless, the goblin "outpost" is the remains of their ship on the tropical Lost Isles. The island you start on is covered in what looks a lot like a jungle with monkeys, terracopters(? – think raptor-like dinosaurs), what looked like pterodactyls flying around overhead, panthers/jungle cats, and huge attacking jungle vines. The reason you're shipwrecked is because the goblin vessel was on its way to Azshara and accidentally wandered into a battle between Alliance ships and a Horde vessel, and the Alliance ships fired on you.

The first three quests you get when you reach the shore are to recover boxes of tools that were stolen by the monkeys, throw explosive bananas at the monkeys to teach them a lesson, and slay terracopters so they'll leave you alone. After doing these and reporting back to your former executive assistant, she asks you to help out goblin miners at a nearby cave. Kaja'mite has been discovered there, but the monkeys are harvesting it with tools (it's speculated that the kaja'mite is having a similar effect to what it had on goblins on them) and attacked the goblins when they tried to retrieve some. You speak to the miner leader and then escort a goblin miner inside the cave where you notice some strange paintings on the cavern walls and find a dead orc carrying a journal. You protect the goblin miner long enough for him to retrieve kaja'mite ore, after which he returns on his own and the quest completes. The wall paintings start a quest requiring you to acquire an artifact belonging to the culture that drew them, which turns out to be a voodoo object belonging to a gnome pygmy/witch doctor (apparently they're not isolated to Outland and Zul'Gurub).

The big quest, though, is the orc journal which you bring back to your former executive assistant. After the Alliance's indiscriminate attack on them, she has decided that the enemy of their enemy could be a friend and sends you to an orc outpost on the island to find out what's going on and see if they need any help. A female orc is in charge there, and she confides that they were guarding a "special cargo" when the Alliance suddenly showed up and ambushed them. She asks you to check in on a hunter she sent out to scout, and you find him and a few soldiers nearby under attack from monstrous jungle vines. Fortunately, you just so happen to have nifty goblin tech available and pull out/create a mechanical weed wacker. A few minutes of spinning fury and 100 chopped vines later, you've dealt with the problem and report back to the female orc. She thanks you and sends you back to the hunter to sweep out SI:7 assassins further up the path past where the (now thoroughly dead thanks to phasing) jungle vines are. The assassins are stealthed, but once again goblin tech comes to the rescue in the form of a pair of infrared goggles. Together with a temporary orc bodyguard, you eliminate x number of human assassins and then report back to the hunter. He expresses his gratitude for your assistance and gives you a panther to ride in a preprogrammed path to the Alliance landing on the beach.

Phasing is once again used, because the orc NPCs at the outpost are now at the beach fighting the Alliance soldiers. You are given a quest to steal a goblin gyrocopter and fly to one of the Alliance ships floating off the coast to rescue the "special cargo" which turns out to be Thrall who's in what appears to be a magical cage. I was in a hurry to finish the quest chain before my play time ran out so I didn't read all of the quest text, but Thrall seems to have been on an important mission of some sort. Anyway, one click and a "Quest Accepted" later Thrall is free and runs to the deck of the ship where he calls upon the spirits and transforms you into a force of elemental devastation to lay waste to the Alliance soldiers. I don't know what happens next because that's when my play time ran out.

Only goblin male character models were playable and the few emotes I tried didn't do anything so I guess Blizzard is still working on them, but I felt that the models had a good degree of customization and still look a great deal like the goblins we've come to know despite the greater detail and the changes Blizzard has made. I didn't see the goblin mount in game, but according to one panel it's a mechanical car/cart of some sort.

All in all, the goblin starting area currently is fun, fast, and facile. The art is vibrant and the entertaining goblin vibe is there, which is important in my opinion, and (at least from the perspective of someone who hasn't played the Wrath expansion) the large use of phasing adds a neat feel to the zone. I also like that you start off as someone who was apparently important before the opening quest.

However, without the intro monologue the backstory seemed a bit lacking (I didn't find out about the slave ship part until later from an orc), and I'm curious how the leveling/zone progression will work. I think Blizzard said somewhere that the new starting zones would be 1-15, and even if goblins start at level 6 by the time my character rescued Thrall he was level 8 and had already explored most of the island which gives me grounds to assume that either there will more phasing, another island (It is called the Lost _Isles_ after all), or an upcoming trip to a revamped Azshara, though if the latter is the case then the Lost Isles would be smaller than any other starting zone currently in the game. A goblin "cannon" type-machine was mentioned at a panel as a way for them to get around too, I think, so it might be possible that there's a second half of the Lost Isles where you're blasted to another island to continue your questing.

Either way, I'm excited about playable goblins and look forward to finding out more about them. I'm even tempted to renew my WoW subscription to try out a goblin hunter when Cataclysm is released, so for the time being they have a thumbs up from me.