I don't believe in "fate," but then, I don't really believe in any external, intangible, independently-acting force.
I don't believe in absolute free will, either, though, because psychological research doesn't support it and our environments impose some restrictions on us. Free will implies that we use our conscious selves to govern our own thoughts, emotions, memories, motivations, sensations, and behaviors; research shows that a lot of this is determined somewhere outside the realm of our consciousness. (In our brains and bodies, still, but not where we're aware of it.) In addition, environment and culture play roles in determining some of this stuff for us.
It also implies that the self is a singular discernible unchanging "thing" that acts as an agent, and I don't agree with that either.
I believe in patterns of behavior, in commonalities in natural laws and biology, in the truisms shown via anthropology and history, in genes and the influence of culture and environment upon them. These things will, out of circumstance, create certain outcomes for certain individuals apart from that individual's awareness and conscious decisions. If that is what you mean by "fate" then...I "believe" in it, I guess, but it is highly changeable and unpredictable. It can be affected by a person's decisions or someone else's. There's nothing that's set in stone: everything is influenced by what came before it, but it is only ever written as it happens.
So, for example, do think if someone went back in time to stop the Lincoln assassination, and succeeded in dealing with the murder would triumph? Or, would fate join in and topple a piano on Lincoln's head?
I don't think "fate" would "do" crap. I do think Lincoln made a lot of enemies and his being assassinated was not unlikely. If it was stopped, someone else might've done it later. Not necessarily, but it's possible. Or Lincoln might have succumbed to his own mental and physical illnesses before his "natural" time. Or he might just have died like any normal non-assassinated person of heart failure or whathaveyou in his old age. No way to tell.