"It's just a wondrous life of unlimited powers"-Max, Three Maxes and a Little Lady
Powers are magical abilities that allows those who posses them to do things ordinary people can't. Powers reside within a magical orb which can be removed, but it seems that the DNA of the owner is what allows the powers to be passed down to other generations.
Because magic is neutral in morality terms, there isn't good or evil powers, it just depend on the user.
Categories of Magic Powers
There's a wide range of magical powers and abilities, which can overlap between categories, fall over into one of the following categories:
SupportingSupporting powers are magical abilities that do not cause damage neither protects, just helps. Those powers are very useful and can be recalled through spells or willingly if the magical creature might posses it. Some of those powers includes teleport, the halo capability to detect Angels or cloning.
Mental powers are magical abilities that allow the user to cast illusions, magically control the body of someone or move object with their minds. Those powers are mostly helping powers, but they can be used in a battle.
Powers related to the four elements are rare. Demonstration of those powers include the elemental spells used in the Wizard Competition or the ability of dragons to breath fire. There are also other powers such as flight, which technically is a air ability, but it's also physical.
Wizarding powers are those powers that require a tool, such as wand or a crystal ball. Those wizarding powers belong, as the name suggest, to Wizards but other magical creatures such as elves can have them. Those powers are used through a set of words, called spells. Wizarding powers are unlimited, except for magical protections or magic-immune materials such as plastic. The powers seem to manifest itself into rainbow colored sphere's throughout the show of "wizards of waverly place" with the exception of "Family Wizard."
Magic powers can, however be removed, because they're contained with a magic orb surrounded by electrical-like sparks. Those orbs can only be removed through spells or enchanted technology. It seems however, that the orb just removes the magic from the previous owner, as Jerry's children still gained wizarding powers even after he gaved up his magical abilities.
List of Powers
This is rather uncomplete