First, I want to make it clear that you shouldn't take whatever info you read here as infallible. There is an element of randomness to the characters and their behavior, and literally anything can happen sometimes, but 9 times out of 10, this is how they will behave.
First, the dynamic duo (because these two seem to sort of work togheder at times):
Bonnie and Chica.Bonnie:
Bonnie the rabbit is the most active character from day one. Bonnie likes to move around a lot and is usualy the first to try and get to you, moving through the rooms and sometimes tampering with the cameras. When bonnie gets to your door, it seems he's that gives you the most time to close your door, and even though he will probably visit you more then once, once he does get there and you lock him out, he doesnt (usualy) stay there for very long.
In the second part of the week, Bonnie gets a weird special ability: he can teleport. As in, Bonnie can be at one room and then suddenly vanish and show up at another room thats not immediately connected to the former, making him a constant threat, since its possible for him to literally teleport from across the building DIRECTLY TO YOUR DOOR. Bonnie does have a certain predictability to him though, since he will always try to get in from the left entrance, and for this and other reasons I'll mention below, you should pay more attention to your left door.
Bonnie also emits a sound when he's teleporting. If you hear a faint distorted voice going "dum de dum", that means Bonnie has probably teleported.
Bonnie will SOMETIMES disable your lights and door buttons. If this happens, it basically means Bonnie is already inside your room and is just waiting for you to stop looking at the camera monitor to attack you, so if your buttons suddenly stop working, you already lost.
Chica the duck (or hen, depending on interpretation) is fairly different from Bonnie. After Bonnie, she's the one that moves around the most during the first half of the week, altough she's a fair bit more "furtive" then bonnie. Chica has an habit of moving, getting to a room and just sort of sitting there, staring at camera, and giving you a sense of safety by not moving for a while, and then moving when you least expect it. She doesnt get to your door as often (in the first days she might not even attempt to) but when she does, she stares directly at you menacingly from the window.
Chica is the only Character that tries to get to you from the right entrance (apart from Freddy in later nights). If you manage to lock her out, you can check if she's still there by using the light and seeing her through the right window. While she doesnt get to your door as often as bonnie, and doesnt seem to have a special hability, she gives you less time to react and close the door on her, and if you manage to lock her out, she will stay there staring at you for a while longer then bonnie, meaning you're going to waste more power.
Chica likes to sneak into your office, like Bonnie sometimes does, disable your buttons and wait till you put the camera monitor screen down to attack you. When she does this, you will hear a faint/distorted "pained breathing" sound while looking at the cameras. If this happens, you already lost.
Chica also seems to like to move through the kitchen (the one room that has no video feed, just audio), so if you hear pans rattling and falling down, someone is crossing the kitchen, and its most likely chica. At times, she and bonnie will get to your door at the same time, meaning you will have to waste a lot of power locking both doors down and waiting for them to go away.
Strangely, chica has a second set of teeth in the back of her mouth. This is never explained, altough it is implied to be the teeth of a guard or a child that got stuffed into her costume.
Now for the less common but more dangerous threats: Foxy and Freddy.
Foxy the Fox is quite a bit different from every other character. When you get to night 2, the phone guy will tell you to keep an eye on the "pirate cove" which is the room with curtains and an "out of order" sign in front of it, that serves as foxy's hideout. Foxy apparently doesnt like to be watched, so in the first nights, you probably wont even see him. You see, Foxy doesnt move around, he just stays behind the curtains in the pirate cove. If you periodically check the pirate cove during the first nights, he wont come out. However, if you check it too much or too few times, foxy will start to come out of his hideout. First you will see his glowing eyes and toothy maw peeking from between the curtains, and later, if he is really comming out, you will find him standing in front of the curtains, in an almost horizontal position, staring at you with his glowing eyes, which are the only things you can see clearly.
After a while, you might look at the pirate cove room and notice he's gone, when this happens, DO NOT LOOK AT ANY OTHER ROOM, just put the monitor down and lock your left door. You see, foxy doesnt roam around, he fucking RUNS STRAIGHT TOWARDS YOU. In fact, if you look at the left corridor camera after he's gone, you will catch him running toward you faster at sonic the hedgehog speed. If you see this, you have just a few split seconds to close your door before he gets you.
Unlike other characters, foxy doesnt jump directly at your face and scream, like the other characters, instead he just pops from the left entrance and stares at you, toothy maw open.
The problem with foxy, however, is that even if you manage to lock him out, he will bang on the doors (foxy is the only character that will do so). While he cant break the door down, somehow banging on the door drains your power VERY FAST, meaning Foxy is a huge threat even if he's much more predictable then the other characters. If foxy gets out from pirate cove, you'll probably lose, either due to him getting you or loss of power, so remember to watch those curtains ocasionaly.
Foxy becomes even more dangerous in later nights, because just looking at his camera a few times may cause him to come out completely. And dont you even try to ignore pirate cove, this will just cause him to come out when you least expect and get you.
Foxy's sound cue is the frantic running sound he makes when he's getting close. After hearing this you barely have a second to close your door. He always tries to get to you through the left entrance.
Foxy also seems to show up quite a bit in the backstory. He's supposedly the character responsible for the "bite of 1987", in which he bit someone's frontal lobe off. Thats apparently the reason why he appears to be damaged and pirate cove is out of order.
I'll post about freddy later since he's the most complex one.