Are there examples of vertebrates with cartilaginous skeletons besides sharks? Would an all-cartilage skeleton be feasible in a land-dwelling animal, which doesn't have the shark's advantage of having its weight supported by the water?

Hi Anna, to the best of my knowledge, besides sharks there are no living vertebrates with an entirely cartilaginous skeleton in the adult form.

The Acanthodii are an extinct group of fish that had a cartilaginous skeleton (they are sometimes called "spiny sharks" but they are not actually sharks).

Many young vertebrates have a cartilaginous skeleton, which becomes progressively more ossified during development. Cartilage is not ideal for tetrapods, since long bones of cartilage are too plastic to cope with the forces of locomotion with deforming considerably. This is probably one reason why the shaft of long bones in young animals is ossified earlier than other bones or parts of bones.

Sturgeons, and their close relatives the paddlefish, also have internal skeletons that are almost entirely cartilaginous. I believe that the skeleton sometimes starts to ossify (turn into bone) in very old individual sturgeons, but I don't know how extensive this is. Lampreys and hagfish have cartilaginous skeletons too, although many biologists would not consider hagfish to be vertebrates in the strict sense - just close vertebrate relatives, our ugly little scavenging cousins.

As you implied in your question, aquatic vertebrates can get by with cartilaginous skeletons because the buoyancy of the water prevents them from having to support themselves against the full force of gravity. A cartilaginous skeleton would be poorly suited for life on land for the general reason mentioned by Paolo, the inability of cartilage to cope with large stresses.

You probably know this already - but just for clarity,  the cartilaginous fishes (Chondrichtyes) include the rays and skates which as well as sharks. Also, inluded are less closely related (and less well known) Chimaeras or ratfish.

It also might be worth noting that many sharks and other cartilaginous fish also calcify their cartilage skeletons. This is a bit different than ossification, which implies the formation of actual bone, with all its complexities. Calcification is just the deposition of bony spicules in the skeleton. It strengthens it, but is not really bone, sort of like the calcified tendons in old chickens and turkeys that people run across as they are eating the drumsticks.