Clearly DKs are still the top of the chart, but not by as much as they once were. Any Tank has self healing now when they need it, and can trade it for DPS when they don't. So safety-wise, they will always be the best choice for soloing simply because survivability is the name of the game when you're going 1v1 against a raid boss.
As DPS/Hard Enrages are the next issue, then offspecs for tanks and pet classes have the power here. If there's something that a tank struggles at because of damage, not survivability, then its likely that a DPS spec or pet class will make it doable. So these are all quite high up in ability also.
Below that comes the various DPS classes, likely the melee ones (Rogue/Enhancement) over casters simply because they have skills designed to keep them alive when things hit them in the face. This will vary by the fight though of course. There are plenty of fights where a caster burning CDs and just destroying something in 30 seconds is preferable.
If you're asking because you want a class to use for soloing from what you already have or want to roll, then pick whichever of the tanks you have/prefer. They're the best bet and each have their own strengths and weaknesses. Druid's come with stealth built in, sometimes useful if soloing content closer to your level since you can often skip a lot of trash. DKs have generally been the first to solo nearly everything as it becomes doable, likely due to their plethora of varying CDs (Not just Tank CDs, things like Army are key to certain fights like pre-nerf Viscidus). Pallies have strong healing in their DPS spec which is downright handy when Enrage timers or DPS matters (Twin Emps). Warriors are my own weakness as I haven't played one end-game since BC, but they likely have their own useful skills as well.