games
Currently, Ashton can be found in two games: Star Ocean: The Second Story (for the Sony Playstation), and Star Ocean: Blue Sphere (for the Nintendo GameBoy Color). Here's some brief info on the games themselves, their plots, and Ashton's role in them. I'll try to keep spoilers to a minimum so you can play and discover on your own, too.

star ocean: the second story
The second game in the SO series, SO2 is Ashton's debut game. Here's the basic story: you play as either Claude C. Kenni, the ambitious (human) son of a prestigious commander of the Earth United Federation and a cadet on his father's ship, or Rena Lanford, an inhabitant of the planet Expel with a curious power and an even more curious past. Eventually, the two meet up (on planet Expel) due to unforseen circumstances, and set off on a journey to save Expel (and, you find, many other planets as well) from the catastrophic Sorcery Globe that is spreading monsters all over. Along the way, they meet up with and recruit several others, including Ashton. Ashton is technically the second character that you can recruit, and does require a little know-how to get everything set up to have him join your party, but is well worth the effort.

star ocean: blue sphere
Set 2 years after the events of SO2, SOBS sees a reunion of all the SO2 characters, and a couple new NPCs and (of course) villains. Now older, Precis and Leon (attending boarding school on Earth) get an SOS message from Opera and Ernest, saying that their ship is going to crash. Concerned, Precis and Leon round up the usual crew (Celine, Dias, and Ashton), minus Claude and Rena, who are currently working for the Earth Federation and off on a mission of their own. Jumping in their own ship, they head off to find and save Opera and Ernest, and find that something mysterious and foreboding is growing on that planet, and planning to take over the universe. Ashton is, as you can guess, a staple character in this game.