I'm playing one currently. A Human Protector Spirit Shaman. I gleefully shouldered the responsibility of the group's lead healer, and so far, I'm really enjoying it. Keep in mind I've only played a level 1 Shaman for one session, but I think I'm starting to 'get' them.
Shamans make fair healers. Clerics, I think, are still the grandmaster heal-bots. Warlords and Bards are about the same (Bards have Song of Rest and the excellent Majestic Word, but few other healing powers they can select, while Warlords can choose to specialize in healing if they so desire). The Shaman's shtick, I think, beyond being one of better healers, is Zones. An awful lot of their powers create Zones until the end of the encounter, and one of their Paragon Paths, the Spirit Tempest, seems to focus on both healing and zones.
I've always enjoyed Zones, as they give you this nice ability to set up a little 'castle' in the middle of the battlefield. As an inherently defensive player, I enjoy this. I think mid-heroic to Epic play with a Shaman will be characterized by setting up multiple, overlapping Zones, stacking crazy bonuses onto your entire party. Since they last until the end of the encounter, you don't have to worry about losing actions maintaining them. Consider Spirits of Battle in particularly. Level 2 Utility, it creates a Zone that gives an untyped +1 bonus to attack rolls until the end of the encounter. Pretty sweet. The best part? It's an Area burst 5 within 10. That is a -huge- frickin' Zone. You should have no problem keeping everyone inside it.
So Zones is one half of it. The other half is the heals. Shamans are interesting because they get surgeless healing as an Encounter power. Their standard heal, Healing Spirit, lets one ally spend a surge, and another ally adjacent to your Spirit Companion regain 1d6. Consider for a moment how powerful that is; if you have one ally out of surges, you will always be able to revive him (out of combat, anyway), provided you have at least one person in the party with a surge left. The ability to 'spread out' your healing is really interesting, fun, new, and useful... but I will admit, I sometimes miss the 'you gain 20 HP in a flash of holy light' Clerical ultra-heals. The Protector Spirit also gets Spirit's Shield, an At-Will opportunity attack that offers more surgeless healing. Cool, but too situational to be a game-changer.
If you're a Stalker Spirit instead of a Protector Spirit, you'll probably be less focused on heals. Instead, you'll be focused on Striker as a secondary role. Not sure how effective that is, so I'll let somebody else comment on it.
What about the Spirit Companion, you ask? The most salient class feature of this very strange class? Well, first of all, it seems to reinforce the "Shamans are all about the Zones" aspect of the class, because the Companion is a zone-like effect in and of himself. Enemies get penalties for being near him, and allies get bonuses for being near him. I've found their At-Wills astounding, personally, Watcher's Strike and Protecting Strike in particular. Their level 1 Encounters and Dailies are less impressive.
Another particularly interesting aspect of the Spirit Companion is that they seem to work like a Swordmage's marks; they're more effective the farther away you are from them. It allows your character to be in basically two places at once. You can have an ally spend a surge on one side of the room, and no matter how far away your Spirit is, another ally adjacent to it can still regain 1d6 HP. It's fun and interesting, but presents some of the same challenges of the Swordmage. Mainly, "How do I get far enough away to make full use of this feature, but without looking like I'm abandoning my party?" During our first session, for instance, the party was fighting a young black dragon. My Shaman sent his Spirit Companion in to fight, and waited safely outside the door, away from harm (while maintaing the necessary LoS to my Companion, of course). Heh, I thought it was cool, but my character might catch some IC flak from the rest of the group for it if he continues such a tactic.
In short:
What I Enjoyed About the Shaman
Reason 1, Zones: If you like Zones, you will flipping love the Shaman.
Reason 2, Healing: Shamans are very effective healers, though not great at 'burst healing', by which I mean bringing somebody from 0 or bloodied back up to almost-full. Clerics are still the masters of this.
Reason 3, Being in Two Places at Once: If you enjoy a little Controller in your Leader and a little peanut butter in your chocolate, you'll be pleased with the Shaman. Like I said, they remind me of Swordmages with their ability to exert influence over two parts of the battlefield at once.
Reason 4, Flavor: Of the PHB II classes, I feel like the Shaman has the most convincingly consistent flavor, despite its complexity. Nothing makes you feel like a serene seer of the spirit world than sitting back and letting your metaphysical lap-dog do all the fighting for you.
Reason 5, Excellent Selection of At-Wills: This is more a comment on PHBII than the Shaman in particular, but I love, love, love that they gave us more than four At-Wills to choose from. They all seem extremely useful, and like a good Wizard, a Human Shaman can target all three NADs with their At-Wills. Sah-weet.
What I Didn't Enjoy About the Shaman
Reason 1, Complexity: The Shaman is definitely an 'advanced class'. It's difficult to wrap your head around it. In fact, I still have several questions, and would greatly appreciate input:
http://www.enworld.org/forum/d-d-4th-edition-rules/252604-shamans-spirit-companion-questions.html
Reason 2, Lack of Focus:
Role: Leader. Your spirit companion bolsters and heals your nearby allies, and you can evoke other spirits to aid your allies and harm your foes. Depending on your choice of class features and powers, you lean toward either defender or striker as a secondary role.
I can sort of understand Defender as a secondary role for a Leader, but I can't understand why you'd try to make Striker work. There are some Striker-ish powers in there, but mostly they seem to be, "Hey, you can be like a Sorcerer, but crappy!" Maybe somebody enamored with the Stalker Spirit path can enlighten me, but color me unimpressed.
Reason 3, "But You're Not a Bard": After the first session, the group's fighter spent about fifteen minutes trying to convince me to reroll as a Bard in order to help his OA-optimized character be moar awesome (since I think he reads these boards: no offense, I know you meant well, and it was great playing with you, and I like your tactical approach to the game. But I'm staying a Shaman, dang it!). Right now, people seem to think that the Bard is overpowered and the Shaman is underpowered. I will concede that, on paper, the Bard seems generally better than the Shaman. It's focused, effective, and powerful. But I think the Shaman brings something new and unique to the table, and I think with time, people will see just how effective they can be.