Various items in Diablo III will often appear with sockets. Sockets are holes in an item that can be fitted with gems (and only gems), which add a wide-variety of bonuses to the item. There are 14 levels of gems, allowing the bonuses to grow quite large.
There are item sockets in Diablo III. Runewords are not returning, but gem sockets can be added to a variety of items regardless of quality of item so a rare or legendary weapon could have sockets added to it. Items types such as Helm, Bracers, Belts and Pants have been confirmed.
No runes in Diablo III are for socketing into skills, not items. Jay Wilson referred to sockets and "gem sockets" in the Gamescom Artisan Presentation video in August 2010 so perhaps that signals a definitive decision made as to what can be put into sockets.have been seen, and
A gem provides different stats based into which item it is socketed, for example, an emerald socketed into a shield will provide some Dexterity, whilst an emerald socketed to a helm will provide Damage Return.
Items with Sockets
Nothing is yet known about the scarcity of sockets; items may spawn with sockets commonly, or not. It depends on how the D3 Team balances them out. It is possible to spend gold to have the blacksmith add sockets to any of the item types that will allow them, so most of a character's gear will likely have sockets, as soon as a player is high enough level to afford it.
The full list of items that can have sockets isn't yet known, but Jay Wilson has said there will be about half a dozen, and we know six right now. (Which might be all of them.)
Other item types may be added, but these are all the Diablo 3 team has yet confirmed.
Sockets spawn naturally in items; magical, rare, set, and even unique items can drop with one (or more) sockets in them. The property is said to be much more common in Diablo III than it was in Diablo II; the team has said sockets are treated much like another affix, rather than being something preset into items by the developers 
- in.Diablo.d3: Can we socket everything in D3?
- Jay Wilson: Not every single slot, but any item the blacksmith can add sockets to, about 6 different ones, he can do. It doesn’t matter the quality of the item. If you have legendary boots without a socket, he can add one.
- Also, sockets can appear on any type of items. On Diablo 2 they only appeared on white items. In Diablo 3 a legendary, rare, anything, can have them. Sockets are treated like another affix.
Adding sockets to items without them is a fairly simple process, one that merely requires gold. The blacksmith offers socketing on his NPC interface, and for a price he'll add a socket to any valid item.
The only demonstration of this yet seen was in the Gamescom 2010 Artistan movie, when he punched a socket into a pain buckler for an exorbitant (according to Jay Wilson) price of 24424 gold pieces. Presumably, based on Jay's comment, the prices are way higher, during this testing period, than they will be in the final game.
The only confirmed socketing bonuses are from an "emerald" as seen in the Gamescom 2010 Artisan video. The gem hover, as seen to the right, granted:
- Weapon: +4% Casting Speed.
- Helms: Attackers take 7 damage.
- Belt/Boots/Body Armor/Shields: +7 dexterity
It's thought that this was a low level Emerald, probably level 2 or 3, though that's not confirmed. If so, it's tempting to imagine how high the bonuses might rise on their way to the maximum gem level of 14. As long as it would take to create such a high level gem (more than 19,600 L5 gems are required to upgrade to a single L14), players expect to be impressed by the end result.