I know, I really spoil you with all these Planetouched posts. But, they're on of my favourite elements of D&D cosmologies (no, it has nothing to with the fact my pageview count and membership jumps with each one I post...)
4e's Genasi are similar to their previous incarnations, though painted in somewhat more generic terms (presumably to help integrate them into different settings). Instead of being imbued with the essence of a particular Elemental Plane, they have been touched by the Elemental Chaos - a mashup of all the Inner Planes, with a touch of The Abyss thown in. While each comes with a distinct manifestation (referred to as (Element)soul, like Firesoul, Watersoul etc.), they are less tied to their element, so much as they are elemental in nature. The extension of this is a selection of feats, and the Elemental Tempest Paragon Path, which allows a Genasi to pick up an extra Elemental Manifestation (or to use two simultaneously) - and I'm torn on this one. It seems pretty cool, and can make for an awesome character concept, but I feel it doesn't fit with the Genasi at all. Each is touched by their element - it affects their personality, outlook on life, everything - and picking up an extra one seems a little schizophrenic in my book. But, fluffwise, it fits - they are touched by a chaotic, ever-changing Plane of the Elements, from which all life sprung - so, sure, they can find a way to branch out.
Fire, Earth, Air and Water are all accounted for - each with some pretty groovy racial Powers - Fire is extra damage (meh), Earth is a little Burst power, which knocks enemies prone (nice), but Air and Water stand out - Water Genasi can shift through any space small enough to allow water to pass, and Air can (kinda) fly - both are pretty handy, and add a lot of flavour and utility to any class. Also added in this incarnation are Storm Genasi - similar to Lightning Genasi (barring those weird crystalline hair-growth thingies), and presumably added for the fact that 4e lumped Electrical and Sonic damage into Thunder damage (a nice little move). Their encounter power is another "adds extra damage to powers with the Thunder Keyword", which is pretty meh, aside from the fact that fewer creatures are immune to it.
In terms of mechanics, all Genasi gain a +2 bonus to Intelligence and Strength - an odd combo, but one which makes them perfect (indeed, the best) candidates for the Swordmage class (also presented in the book). A sort of gish-style Warrior Mage, Swordmages are a lot of fun in play (lots of teleporting, forced movement, marking, and fun elemental effects). They also make good Wizards due to the Intelligence bonus, or Warlords who can throw out a few extra hits.
Their new artwork (and attached fluff) makes out they are all pierced, tattooed, and bear unique skin markings they just love to show off. While I understand 4e's default assumption is TITS AHOY! (see: Hot Half-Orcs, Breasts on Dragonborn, Breasts on LIVING CRYSTAL PEOPLE), it's kinda annoying that all Genasi are marked the same. I would have assumed that Fire (passionate, fun-loving), maybe Air (wearing lightweight clothing anyway), might do so - but an Earth Genasi strikes me as quite well-covered, for example.
All in all - a nice little race (or set thereof), with some interesting options and abilities. Shame about the fluff, but hey - that's what DMs are for!
Next, the Abyssal Genasi - corrupted, warped counterparts to the normal manifestations!