A thickness of 1.5 inches is the standard for concrete countertops. Concrete allows for surprising strength and durability even at this relatively shallow thickness. Two inches is the next most common thickness. It, too, will provide plenty of strength against dropped pots and pans, or even the elements in the instance of outdoor bars. A sturdy, well-maintained cabinet is essential even for a 1.5-inch slab of concrete. As long as the cabinet doesn't have any obvious flaws or damage in need of repair, it will hold.
Sometimes people want a thicker countertop for aesthetic reasons. For instance, a 6-inch concrete countertop is not unheard of and is doable. The entire countertop will not be 6 inches thick; only the front part of the counter will be 6 inches, while the middle and back are 1.5 inches. This allows it to sit atop a cabinet without pressing down on it with too much weight while still giving the illusion of a countertop that is 6 inches in depth throughout.
A standard concrete countertop weighs 18.75 pounds per square foot, according to the Concrete Network. This is a bit heavier than granite, which weighs 18 pounds per square foot. While lightweight concrete is available, and is sometimes used, it is not as strong and durable. In most cases, regular concrete is preferable to its lightweight counterpart. The Concrete Network points out that standard cabinetry will support the concrete because the weight of it is spread out over a fairly large area. If your cabinetry supports granite, then concrete should be no problem.
In most instances, the 1.5-inch standard thickness concrete slab will suit your interests. Since it's the standard, you should have no problem finding it and it is cheaper than the thicker alternatives. If you have the money to go for a larger thickness for aesthetic purposes, just remember that the majority of it will be 1.5 inches and won't actually be sturdier or stronger than the standard. The following will also raise the cost of concrete countertops but may be desired by the homeowner: irregular shapes, drain boards, custom edges and back splashes.