Economists classify goods on a public-private spectrum based on the extent to which they are rivalrous and exclusive. Exclusivity is based on how easily one can be prevented from enjoying a good, and rivalry is based on whether my enjoyment of the good prevents you from enjoying it. National defense is a classic public good: any number of citizens can benefit from it at once, and there is no way to keep someone from enjoying the benefits. Food is a classic private good: we cannot both eat the same bite of food, and there are a variety of ways for me to keep you from eating my food.
Different MMOs place their mobs at different points on the public-private spectrum. In the early days, mobs tended to be rivalrous but not exclusive: whoever got the last hit got the prize, no matter who dealt the most damage, tanked, etc. The reigning solution to the problem was tapping so that you could claim property rights on an enemy, but claiming a camp was a matter of social convention rather than game mechanics. If you tapped the mobs out from under someone, they were yours. Instanced enemies are exclusive. Guild Wars 2 took the unusual step of making mobs mostly non-rivalrous: until the enemy runs out of hp, we can all get all the benefit from it. There is still some rivalrousness in the race to tag enemies or get to the event boss before it falls, but everyone in the fight shares in the fight. [Update: commenters have noted that other MMOs have followed suit to varying extents.]