This discussion may contain spoilers!
Personally, I think a couple of fables mentioned are deemed liable suspects, while others are not. Here is a quick overview of every character. Any opinion with # at end is definite.
Bigby: He was asleep at the death of Faith, and arresting Dee/The Axeman (whichever you chose to arrest) at the death of Snow aka Holly's sister, Lily. I believe he is innocent, but there is always that slim chance that he killed Faith in his sleep and killed Holly in some mid/cutscene. Real Snow asked at the sight of Faith's death "What Could Have Done This?" he replies "Something very Sharp (HIS CLAWS, such as when he tore off Gren's arm in the fight) or something with magic attached to it". However, until more evidence is shown. I believe he is innocent at this point
Snow: Little bit of speculation at this point, not yet sure if she is the murderer, as she is separated from Bigby at every crime scene and happened to be the one to find the head. Nevertheless, I believe she is 100% innocent
Detective Brannigan: Although we don't know much about this character, we know that she also has access to case files and information, and would also have the best experience to pull off a murder without getting caught. She is a liability. I don't think, however, she is a suspect at this point as there is no criminating evidence and little background surrounding her character. If she appears again, then yes, there is a more significant probability
The Boy Who Cried Wolf: Here is an interesting character, with definite suspicion surrounding the case as he appears in many scenes in Episode 1. He is shown at the beginning, driving the Taxi, generally appearing in multiple scenes and is even knocked down during the chase sequence with Dee. This, as a result, is the first #SUSPECT
Crane: Definitely something fishy going on with Crane. However I believe he is innocent. He fantasizes about sexual relations with Snow, and as a result has turned Lily into Snow. Maybe he is just running in fright of the consequences. However, this does not explain how all the blood got on the bed. I believe someone else snuck into the room and murdered her after Crane had left, which I will cover below. However, crane is still a potential suspect.
The Woodsman: We first met the Woodsman beating Faith in Episode One. He is seen as aggressive and is the first character we are introduced to being the suspect in the series. Faith's death would leave him as the prime suspect, with motive, and the blessed axe for the head dismemberment. There is also the option to arrest him or Dee at the end of Episode 1, and regardless of which you arrest (Axeman or Dee) Lily dies anyway. Also it would be far too cliché for the murderer to be framed and suspected by Bigby in the opening episode. #INNOCENT
Dum, Dee + BOSS: 100% Innocent, I can guarantee that while there is suspicion around these guys, again it would be far to cliché and easy to name these guys as the murderers. I believe the boss also has the same motive as Bigby, to find the Killer. So I believe these 3 are innocent.
Bluebeard: Introduced in the second episode, he is seen beating Dee for information. While he may seem aggressive, I believe he is innocent. There is not a lot of background on this Fable, however.
Beauty and the Beast: Now HERE is an interesting case. There isn't a lot of background on Beast yet, so I'm completely unsure about him. I am skeptical however, if he didn't know where Beauty was, then what on earth was he doing in that building where he met his wife and Bigby? He just happened to be wandering the second floor casually?. However, his wife Beauty, Has A LOT to answer for. Firstly, we now know where she was headed off to in EP1, to the 'Working Girl' building, working there as a receptionist/admin. The Lily Murder (coming back to the Dee/Dum case) is very speculate around her. She has a key to the room, and Bigby doesn't recognise any forced way of entry into the room, meaning whoever was in there had access to the key. This makes her the perfect candidate. Another pointer here, not saying it is her, But someone is in the room with Crane, which funnily enough noone has seemed to pick up on. It's a photograph with Crane putting BOTH of his hands on Lily's body, meaning he didn't take a 'selfie'. Someone was actively taking pictures in the room, meaning a second person was in there unless the camera was on a timer, but now I'm getting too technical. However, getting back to Beauty, she is mentioned by Dee and therefore suspected, and as a result, cures part of her innocence, but at this stage, I believe she is some way tied with this, and so is titled a #SUSPECT
The Crooked Man: I see a lot of people talking about him, and have no idea who he is, unless it is AKA the Boy Who Cried Wolf, so I cannot speculate on his case or already have.
Holly: What better way to save your own skin then kill your own sister, it makes her look innocent. However she was with Bigby when Snow AKA Lily was killed, so unless she has an alias, for now, she is innocent.
Gren: Vicious individual, but hates Snow and cares a lot for Holly, so if he wanted to kill Snow, he wouldn't kill a fake snow white which ironicly enough ended up being holly's sister...OR WOULD HE? Apart from this, we know nothing about this character. So until proven guilty, innocent for now.
Narissa AKA The Little Mermaid: We were just introduced to her, yet there is little doubt in my mind that she is the killer, although she worked with both of the dead fables (Faith and Lily) I believe she is innocent as she gives hints to Bigby, although this could be a wild goose chase.
Georgie: Sure, He's a pimp. Uncaring, rude and unwilling to cooperate on solving the murder, but I believe he is innocent, as again, it would be too cliche.
Bufkin:No idea what to put here, any thoughts? Leave in the comments below.
Colin: I thought it was strange, and I don't believe people are paying enough attention to this character. He is first seen in Bigby's apartment. They talk, and then settle down for some rest. Now here is where it gets interesting, COLIN is GONE when Snow starts knocking on the door, and Faith's head is on the doorstep. What's stranger is we haven't seen him all of Episode 2, yet somehow Lily winds up dead. Now I don't want to go pointing fingers yet, but in my books DEFINITE #SUSPECT
Finally, the ONE FABLE I have had in mind from the beginning that noone else has yet suspected or investigated....TOAD
Mr. Toad: Now who would suspect the quiet, innocent, always calling for the Sheriff toad that gets beat up and has people sneaking through HIS APARTMENTS (Dee). Now although Dee said Faith stole something from his boss (which we are not yet sure what it was, yet I believe it would accelerate dramatically the crimes, acting as a crucial part of evidence) he was still snooping around the apartment, and may have been coached to tell Bigby he was looking for a stolen item. Now although I said the Woodsman was the first character that is a suspect, the VERY FIRST CHARACTER apart from Bigby that we are introduced to is Toad, which obviously has a grudge on Bigby shown through his attitude as Bigby keeps telling him to get a glamour "Dont make me ask again" in the opening sequence of episode one. in MOST GAMES, there is a CRUCIAL part played in the opening sequence, which noone surprisingly seems to have picked up on. Thus, I am naming Toad as a #SUSPECT
EDIT Just thought about one last character, Mayor Cole:
What's strange about this is he has recently left (not specified by Crane in EP1 where exactly 'The last thing i need with Mayor Cole away is a hysteria! Do you understand me?') we just know he is temporarily 'away'. Now here's something I picked up from a couple of characters aswell. Snow says things are worse than ever in the cab ride with Bigby, and bigby says they've been worse, she says 'not by much'. Funny that, isn't it. As soon as the mayor goes 'away' 2 dead bodies? hmmmm.....
Gren also re-affirms my theory, after Bigby first meets him in the bar and calls snow a bitch 'Holly's sister goes missing and noone gives two shits about her, paperwork, waiting rooms...' meaning that she has been missing for a while...
The last shred of evidence is the photograph of Crane molesting Holly's Sister. Crane would not leave photo evidence behind of him doing that, he has certainly been framed and someone has left the photograph there afterwards, but how the photo got taken in the first place if Crane wouldnt allow it... only one way. Crane wouldnt let anyone in the room to take the picture, so someone would have taken a picture through the visual of the mirror. And who else would have access to Mayor Crane and Snow Whites Office? Mayor Cole....
Personally, believe what you want. Those are my suspicions and opinions at this point of time, please feel free to clarify me in any false information provided or any missed information which can also narrow down the list of suspects.