Most players (especially tamers) rely on pets to some extent or other. Warriors require Horses and Swamp Dragons to ride on, while Pack Horses and Giant Beetles are of great use to resource collectors and crafters.
Originally when a pet died a new one had to be purchased or tamed, however eventually pet bonding was introduced. In addition to allowing you to salvage your dead pets a nearby bonded creature will recall with you (regardless of whether you are riding on it or not).
In order to bond a pet you must first feed it. After a week has passed in real time, provided you have enough taming skill to reasonably control the animal, feeding it again will bond it to you. A bonded creature will display the title "(bonded)" under its name instead of "(tame)".
A bonded pet, when killed, turns into a ghost that will accept non-combat based commands. It cannot target or be targetted while in this form, nor can it be stabled . A player with Veterinary skill is capable of resurrecting the creature. However, as a result the pet will lose 0.1 from any skills it had prior to death.
These skills can be trained back to 100 or whatever they were when the pet was first tamed (whichever value is higher). Pet deaths do not affect their stats or resistances.