Disclaimer: It should be noted upfront that this post mainly concerns cooling with an eye toward overclocking. If you intend to keep all of your components at stock clocks, it's unlikely you'll need to bother with aftermarket cooling of any kind. If your intent is to utilize aftermarket cooling to achieve a near silent PC, please ask in the thread for recommendations.
As mentioned in the last post, cooling your PC realistically comes down to Air or Water for those of us who don't feel like hacking up a refrigerator or utilizing Peltier effects. If you decide on "Water," you need to know that you're looking at two options built on an identical process, with significant differences in design. The decision comes down to a choice between a custom water cooling loop, or a "closed-loop" cooler.
Custom water-cooling encompasses a vast and varied market of products. There are 4 main components for a custom loop, a radiator, a pump, a reservoir, and "waterblocks." The function of the radiator, pump, and reservoir are relatively self-evident. "Waterblocks" or just "blocks" are heatsinks applied to the various components in your PC for water to run through. These include the most common components, CPU and GPU blocks, and more esoteric products, like waterblocks for motherboard chipsets, RAM, and even HDDs. The basic idea of a water cooling loop is that a liquid (distilled water, or another liquid coolant) is pumped from the reservoir, through a tubing into waterblocks, where is draws heat away from the blocks and into the flowing liquid, which then leaves the blocks and enters the radiator, where the liquid is cooled, before heading back through the pump to the reservoir, etc. etc.
Because liquid is a significantly more effective conductor of heat than air, and because custom-loop radiators often have significantly more surface area than an air-cooler, water-cooling is a significantly more effective method of cooling your CPU and GPU(s). Components like drives, RAM, and your motherboard chipset don't usually demand more than passive cooling, so they are usually the last components to be considered for inclusion in a loop.
The main advantage of custom water-cooling is that it's a more effective method of cooling PC components, especially in higher overclocks. Because of the sheer surface area of some radiators, lower amounts of airflow are often required to go through the radiator, which results in many custom loops being quieter (relatively speaking) than higher end air cooling setups.
Disadvantages of custom loops include expense, which is usually significantly in excess of even the highest end of air-cooler designs. A custom water cooling loop requires significant research to develop the knowledge and skills to ensure it is built correctly. A custom loop also generally requires much more significant time investment in the building stage, first when installing the loop and then when leak-testing the loop. Custom loops also require regular maintenance, in excess of the standard dust removal procedures, including regular refilling, and (depending on the liquid used an precautions taken) cleaning of the loop.
Recommendations: Discussing and recommending custom water cooling kit could be an entire blog unto itself. I'm not qualified to make particularly good recommendations on this score, but I can point you to some good resources if asked.
Closed-loop coolers and custom loops are based on an identical set of components. Just like a custom loop, a closed-loop cooler has a pump, radiator, reservoir, block, and tubing. The difference is that a close-loop implementation combines some of the elements (usually a reservoir/radiator combo and a pump/block combo) and then seals the entire thing up.
Closed-loop coolers are almost universally CPU coolers. A few specialized GPUs are sold with closed-loop water coolers for cooling, but this is a relatively recent implementation that hasn't yet become widespread. Asetek and Coolit are the OEMs behind the vast majority of closed-loop solutions, most (if not all) retail closed-loop implementations are rebadges of their products, or products designed and produced for the retailer by these OEMs.
Closed-Loop products are favored by many "boutique" PC retailers (like Cyberpower) as ideal solutions for gaming PCs. They're often as quiet, if not quieter, than traditional air cooling setups, and allow them to advertise that the CPU is water-cooled without the time, mess, and expense of a custom cooling loop. By virtue of their design, closed-loop coolers are much less prone to leakage than custom loops, and don't require maintenance (aside from standard dust removal measures). Because the waterblock/pump assembly is so small compared to virtually any good air cooler, closed-loop solutions are excellent for situations where you wish to avoid RAM clearance issues, or have limited clearance above the CPU socket (as in many small-form-factor cases).
Disadvantages for closed-loop products include price/performance. Many budget-friendly air coolers will match or outperform a significantly more expensive closed-loop cooler. In general, the best air-coolers will outperform the best closed-loop coolers. Depending on case design, the reservoir/radiator may cause clearance issues with various components. A closed-loop cooler is not competitive with custom water cooling loops. A custom loop generally has more liquid, a better pump, less restrictive blocks and tubing (which improves liquid flow and cooling capacity) and significantly more radiator surface area.
Recommendations: I prefer the newer generations of Corsair closed-loop coolers. They combine solid installation (as opposed to the ludicrous circular ring mount of earlier efforts) with solid performance and a fairly good range of prices. The H60 is a basic thin-rad, single fan setup. The H80 has a thicker radiator and 2 fans. The H100 is the highest end, boasting a 240mm radiator and 2 fans (with a max of 4 fans for push/pull). If you want a closed-loop cooler, pick the one that best fits your needed level of cooling and maximum level of expense.