The only game I know of that was remade TWICE.

User Rating: 9.5 | Chrono Trigger DS
Yeah, this game was released on the SNES, then remade for the PS in time for Chrono Cross. Then, released once again, on the DS.

Chrono Trigger has to have one of my favorite battle systems EVER.
No random battles- sometimes. By sometimes I mean that sometimes enemies jump out of no where. But, they ALWAYS jump from the same place, so you know where the enemies are once you've fought them.

So the story is that your friend, Lucca, made a teleportation device.
Then someone you bump into, Marle, gives it a shot.
Her necklace, however, seems to have made the teleportation device malfunction somehow, and teleported Marle back in time to 600 A.D.
Later, in 2300 AD, you see that the world is in ruins and there are few humans.
You find out that the world ended in 1999(I laughed at that part :D)due to some creature called Lavos. The rest of the story is you and your party going to different times and places to save the future from Lavos.

I'm going to list the playable characters here.

Crono- The main, silent, protagonist. His time is 1000 AD, the present in this game.
Lucca- Crono's best friend. Her time is 1000 AD.
Marle, a.k.a Princess Nadia, is a princess of 1000 AD.
She is very tomboyish, however, and longs to get out of the castle, so she sneaks out for the Millennial Fair.
Frog, a.k.a Glenn- He was originally the brother of Cyrus, a brave knight, until Magus killed Cyrus and turned Glenn into a frog. He is now a brave knight of 600 AD.
Ayla- A very strong girl, who isn't afraid of anything. Her vocabulary isn't too great, though. She is a chief of a tribe in 65,000,000 BC.
Robo, a.k.a R66-Y- He was created, then abandoned. Not much is known about this robot, other then that he was fixed in 2300 AD by Lucca.

I believe this guy, you can get him, or skip him.
Magus- Originally from 12,000 BC, his real name is James. When Lavos escaped, he was teleported to around the late 500's AD, and is now the Fiendlord of 600 AD. He was thought to be a villain, but it is revealed he is just trying to destroy Lavos.
Magus has one of the most confusing back story's in the game.
Ugh..
Here are the times-
65,000,000 BC- A fight for the greatest species, between humans and reptites.
12,000 BC- A segregation between magic users has put the non-magic users into the everlasting blizzard below, while the magic users made cities and a palace in the sky.
600 AD- A war between humans and fiends, basically.
1000 AD- No wars, no fiends. A peaceful time.
1999 AD- The Day of Lavos. The world ends.
2300 AD- A ruined world, destroyed by Lavos.
Infinity- The End of Time, where every border of every time meets.

This game is definitely worth it.
:DDDD