|Source: Microsoft Clipart|
The most commonly discussed storage method involves batteries. There are many well-established battery technologies that can be used immediately. However, these existing technologies are expensive. Utility-scale batteries are being researched in an attempt to lower costs and raise capacity. This is the tactic that Elon Musk of Tesla Motors has taken. Tesla lowered the cost of utility-scale storage to ~$250/kWh.
Even within battery technologies, there are a variety of options, some more in development than others. Elon Musk and many other companies use lithium-ion batteries. Lithium-ion batteries are currently the market leaders. For off-grid and some utility applications, people often use lead acid batteries (basically, souped up car batteries) due to their low cost. Flow or sodium sulfur batteries may be used on utility scales. Sodium sulfur batteries require higher temperatures for operation. These technologies are promising due to their cost, energy density, and lifetime.
There are other technologies out there that might offer more significant cost benefits down the road. For solar thermal power, one might combine solar thermal power generation with hydrogen generation and use the hydrogen as a storage medium. This hydrogen can then be used for industrial uses, turned back into electricity using fuel cells, and/or used for transportation purposes.