I'm not sure if they should have gotten together. But I see a lot of people say they had no chemistry together, and I have to disagree. I think they had too MUCH chemistry. Perhaps they had too much of a fiery dynamic to ever be good together in a relationship. But they were totally into each other.
There is endless evidence of Faye liking Spike, anyway. Her crying when he goes to die, well you could say that's just because they're friends. She acts all tough, but a few times you see that she tries to keep Spike from doing stupid things and getting hurt. Despite her snide comments about him being a walking accident, she does stay by his side while he's unconscious. But the most overwhelming bit is the episode where Faye finds out about Julia. When she's in Jet's ship, on the way back to the Bebop, she asks who Julia is, and when Jet says she has some kind of hold on Spike, she looks really depressed. And later, when Ed is painting her nails, she randomly says "Julia", and when Ed asks, she says she was "just thinking about someone." I'm betting the someone here was Spike, not Julia. (Incidentally, I think her saying "Oh Ed, anything but blue." is prophetic; when Spike dies, the song playing is called "Blue". Or at least it's a symbolic with all the other times blue is mentioned.)
As for Spike, it's hard to say how he feels about Faye. He flirts a bit. When he says something about not coming back from his fight with Mad Pierot, he says "Just kidding. Would you rescue me if it were true?" in a taunting sort of voice.
He knows how she feels.
Most of all though, in the last episode, before he leaves to fight Vicious, they have a telling moment. He tells her to look into his eyes, tells her about them... and when he says "I have to do it, Faye", I see in his eyes another unspoken statement: I know how you feel. If I wasn't so obsessed with this one thing, I could like you too. But I have to go now.
What do you think?