Snubbers
Snubbers are a dedicated device for shock absorption, an option if not enough rope is deployed as part of the main rode to naturally achieve this important functionality. All small boats require some form of shock absorption, to avoid placing shock loads on the rode as the boat pitches and veers. Such shock loads will otherwise either result in far higher peak loads on the anchor, so increasing its chances of dragging, or over-stress the chain.
Snubbers reduce or eliminate noisy 'chain rumble' and noise which travels as vibrations up the chain. This sound can otherwise be quite severe in the forepeak or forward berths of a boat. On the other hand, while some boaters find this irritating, this noise can also provide feedback regarding what the chain and anchor is doing on the seabed.
Rope
Rope snubbers are just a length of nylon which takes the load off the chain. Enough slack should be in the chain that the rope can properly stretch (do not underestimate this).
Manually tying the line to the chain with a rolling hitch is suggested as a preferable alternative to a chain hook. This does not stress the chain as much as a hook can. A rolling hitch, which retains most of the strength of the rope, takes a little longer to attach and remove, but does not wear the chain and tends to spread the load over multiple links of chain. Tie the rolling hitch around the exterior of a link of chain, then secure the working end with one or two clove hitches further down the chain. The clove hitches have no need to be tightened.
A chain hook can also be another 'weakest link' factor in the system, as some claw types made out of bent bar will open up under strain. Often the rope is spliced directly through the hook eye, which then forms a weak point – rather, it should be spliced through a thimble and joined with to the hook with a shackle (which in turn can be a weak point and should be of maximum quality). Bear in mind that chain hooks can place adverse strain on a single link of chain in a direction for which the chain was not designed. Additionally, a metal claw working on a chain link is hard on the galvanizing and will result in substantial wear.
Rope used as a dedicated snubber should be sized according to the conditions and the vessel. In general a minimum of 10 m (30') should be employed, or a length of half the LOA of the vessel, whichever is longer. A shorter snubber (depending on the rope diameter) does little with regard to shock absorption, but it will serve the purpose of stopping chain rumble and roller noise.
As with all rope, a good solution for chafe protection is absolutely critical.
For more, refer to the Rope section.
Rubber snubbers
Special purpose rubber snubbers are commercially available, designed for this purpose. They allow the snubber to be shorter than a rope length, helpful in shallow water or crowded anchorages, and also greatly minimizing the slingshot effect which long lengths of nylon can introduce. They are typically integrated with a short length of rope, so the attachments (to the chain and the boat) are no different.