Hey there! You have found your way to the fanlisting for the relationship between
Faye Valentine and Spike Spiegal,
from the amazing animanga Cowboy Bebop.
In the year 2071, the crew of the spaceship Bebop travel the solar system trying to apprehend bounties. In the slang of the era, "cowboys" are bounty hunters, hence the name of the series. Each member of the Bebop crew contributes their own unique abilities to help catch bounties. Most episodes revolve around a bounty; however the real focus of the show concerns the pasts of each character, which unravel and connect as the series progresses.
Arguably, the main plotline focuses on Spike Spiegel, a former member of the 'Red Dragon' crime syndicate who is haunted by a past love triangle between his former syndicate partner, Vicious, and a mysterious woman named Julia.
The series also focuses on the histories of the other Bebop crew members: Jet Black, a former ISSP officer on the Jovian moon Ganymede; Faye Valentine, an indebted gambler recently awakened from cryogenic slumber; Edward, a genius girl computer hacker who can hack at 10 times the speed of an expert hacker, and Ein, a revolutionary "Data Dog" (super smart dog) capable of countless amazing acts.
As the series progresses it starts appearing that Faye may indeed have started having feelings for Spike. Though this is never stated, her attraction is implied by her interactions with him (Pierrot Le Fou, My Funny Valentine, Speak like a Child) as well as her fascination with Julia (Jupiter Jazz, The Real Folk Blues).
People assume Spike does not reciprocate the same type of feelings for her because of his decision to seek Julia and face Vicious in the final episodes. I, however, fully disagree with this theory. Spike himself stated that he wasn't going to die but to find out if he is really alive. I translate this into him telling her he can't look to the future, whether with her or alone, until he settles his past.