Gamethyst (also known as Amenet and Sugilite) is the ship between Garnet and Amethyst.
In "Coach Steven", Garnet chose to fuse with Amethyst, regardless of Sugilite's instability. Amethyst was very excited to do this, going to the extreme of screaming in happiness.
In the same episode, their fusion dance is revealed to be very suggestive.
In "Mirror Gem", Amethyst held onto the inside of Garnet's leg and said, "Garnet, do something."
In "Cheeseburger Backpack", Amethyst fell into Garnet, though this was probably just because the tower was collapsing.
In "Arcade Mania", Amethyst wouldn't deny that Garnet was "the boss."
However, this may have just been to prove Pearl wrong.
In "Tiger Millionaire", when Garnet said "Amethyst, you are a Crystal Gem. You need to act like it.", she seemed very shocked at Garnet saying this, and sounded pretty sad as she went into her room.
In "Laser Light Cannon", Amethyst wanted Garnet to keep throwing her into the Red Eye.
In "Steven's Lion", Garnet teased Amethyst, who didn't seem very upset about it.
In "Steven The Swordfighter", Garnet and Amethyst were together for most of the episode.
In "Lion 2: The Movie", Garnet seemed to like Amethyst's music.
In "Keep Beach City Weird!", Garnet joins Amethyst in shape shifting into Steven and plays Steven Tag with both of them.
In "So Many Birthdays", Garnet rides Amethyst (who is shape shifted into a tiny car).
Also, to top it off, after Amethyst reverts to her normal shape, Garnet is seen sitting on top of her.
In the same episode, Amethyst feels guilty when Garnet cries.
In "An Indirect Kiss", Garnet pulled Amethyst's top down without warning, causing Amethyst to blush. It also seemed like she couldn't bear to see Amethyst distorting, as she was the first to walk away when Pearl and Garnet tried to fix the fountain.
Amethyst, known for being the rebellious type, follows Garnet's orders nonetheless. This shows her true respect for Garnet.
Throughout "Reformed", Amethyst constantly tries to impress Garnet by changing her form to what she thought Garnet might like.
In "Sworn to the Sword", Amethyst's temple door opens revealing Garnet and Amethyst together, while Amethyst laughs at Garnets implied joke, saying, "Wow Garnet, that was the funniest thing I've ever heard!"
In "Cry for Help", Amethyst's song, Tower of Mistakes is about her wanting Garnet to forgive her for what happened when they formed Sugilite. In the beginning Steven suggests they form Sugilite and Amethyst says "Yeah, I guess that's Garnet's choice" and seems shocked when Garnet rejects her.