Elementals are a common monster that you can see a mage summon. They are a concentration of energy of a specific element. Some Elementals are a concentration of various plants or objects. Examples being the Thorn Elemental from the Magic Multiverse and a Sword Elemental that is made up of multiple swords.
The most common Elementals are the usual Fire, Ice, Water, Electric/Thunder, Wind, Earth, Light, Dark and Shadow. More advanced ones that are a bit more uncommon, but not exactly rare are the Holy, Unholy, Hellfire, Fusion and various combinations of elements.
Worlds known to have Elementals of some kind are:
Interworld System of Planets
.hack
Digimon
Final Fantasy Universe
Heaven
Hell
Card Captors (in the form of Clow Spirits)
Dark Cloud
Dragon Quest
Duel Masters
Magic
Oblivion
Purgatory
Shadowverse
Skylanders
Suikoden
Yu-Gi-Oh