Who Has The Infinity Gems, and What Are They?

Marvel MCU All Infinity Stones

The Infinity Gems (or Infinite Stones for the Marvel movie universe) are the most powerful items, or collectibles, in the galaxy, and possibly the universe. In Marvel comics there are six infinity gems, but no one is certain if all six will be in the movie. We expect six, because of The Collector saying so in Thor: The Dark World.
First, lets look at the Infinity Gems in the comics.

Soul Gem (Green)
This spooky gem has the power to control souls, and summon the dead. The power is said to be created by the gem’s cravings and manipulation of souls.
Dr. Strange currently has the Soul Gem.

Time Gem (Orange)
The time gem is used to control time, allowing time travel, and also immortality or a longer life span.
I believe Captain America last had the Time Gem.

Power Gem (Red)
An extremely dangerous gem in the wrong hands. Well, I guess all of them are, but the power gem allows use of practically any powers, super or natural, by its wielder.
She-Hulk had the Power Gem, but gave it to Namor.

Reality Gem (Yellow)
A dimensional type gem that allows travel from different plains of reality, this gem allows its user to visit places never even considered.
Iron Man currently holds this gem. And it matches his suit!\

Mind Gem (Blue)
This gem allows mind control, mind reading, and can also be even better with people already using such powers.
Professor X currently has the Mind Gem.

Space Gem (Purple)
This gem is used for traveling to any location in space. It also allows omnipresence and duplication.
Black Panther currently hols this gem.

Before getting into the movies, let’s have a quick history of the gems. The gems are most known for being used by Thanos to create the Infinity Gauntlet, the most powerful weapon in the Universe. Each gem is powerful, and becomes more powerful when used with others. So you can imagine the damage it almost caused in the hands of the death obsessed Thanos.

(See this post for Infinity Stones in Marvel Movies)
I will say there are two so far, the Space Stone (Tesseract) and the Power Stone (Aether). Featured in Avengers, Captain America, and Thor 2: The Dark World. 
A third is said to show up in Guardians of the Galaxy.