Water stones are messy (as they must be stored in water, used wet, and occasionally flattened). Likewise, oil stones require honing oil which can be a bother. Abrasive papers wear out (meaning there is a large hidden cost). Diamond stones are convenient because they only require a bit of water as lubricant and don't need flattening. They are, however, somewhat expensive.
Spyderco is now offering ceramic sharpening stones. These new ceramic stones seem to have everything going for them: no oil, no water, no wet storage, no flattening, no replacing paper. They require only the occasional cleaning with an abrasive kitchen cleaner (Comet, or the like). They are fairly affordable to boot!
Note that Spyderco has the traditional flat stones (right) for sharpening chisels, planes, jointer blades, and knives. In addition, they are have a set of specially shaped stones (left) for sharpening odd shaped carving tools.
Check out the new Spyderco Ceramic Sharpening Stones.
Here's a video on the product courtesy of Woodcraft Woodworking Supply.