Fire Gem: The fire gem is very dangerous and is only handed to people that will be responsible with it.... or maybe not. With it, you can control fire and be invincible to it, or something like that. With this, you could get a complete random hybrid, except for a water animal.
Water Gem: This gem is one of the more rare of the most common elements that people think about. With it, you will be able to do something like controlling tides and weather or be able to play with the water. Or, you could be a hybrid with an animal in the water.
Air Gem: This is one of the most common gems you can get. With this gem, you will either have a power that can help you control what happens with the wind or make you fly or something along those lines. Or, you could have a hybrid with something that flies.
Earth Gem: The Earth gem is also very common. With this gem, you could have something similar to the ability to heal or grow things in nature, or cause earthquakes and other natural disasters. This power is very rare and only the most experienced can do this. You might get a hybrid that is a land animal and powerful in forests, like tigers or foxes.
Void Gem: This gem and the darkness gem are the two most powerful gems there are. They are EXTREMELY rare and super powerful. With it, you could create a black hole or a sinkhole, or make people in a coma. Your hybrid will usually be something mythical, like an alicorn. Don't get your hopes up on getting one, and asking for it makes your chances even worse. Only special people that will change these freaks' rights might get it. Might.
Frost Gem: The frost gem will give you a power that is related to either snow or ice. You might be able to control the weather or build a snowman with the snap of your fingers. Or, you'd get a hybrid that lives in the arctic.
Sun/Light Gem: This gem will either give you powers that will bring light to dark places or cheer people up, for the most part. If you get it, you could also warm things up. Your hybrid will probably be an animal in the desert.
Darkness Gem: This gem is also super duper rare and extremely powerful. You can set curses on people and other things based on darkness. Your hybrid will usually be something mythical, like a dragon.