Overall, many people are shot throughout the series, some at point blank range, and sometimes there can be very graphic results (blood splatter, occasional gore, visible bullet holes, etc). In certain episodes, corpses are melted/dissolved, and some of these scenes can be very gory and graphic. Notable instances of violence are mentioned below:
Season one, episode one ("Pilot"): Character attempts suicide, but his gun is on safety.
Season one, episode two ("Cat's in the Bag..."): the last five and a half minutes of the episode consist of a body being dissolved in acid. This is gory, graphic, and will likely be disturbing to several viewers.
Season one, episode three ("...and the Bag's in the River"): the first three minutes of the episode, before the title sequence starts, consist of the characters cleaning up dissolved body parts. In one of the last scenes, a man is choked to death with a bike lock. Lasts for about 20 seconds. The man stabs the attacker in the leg with a broken piece of plate before he dies.
Season one, episode seven ("A No-Rough-Stuff-Type Deal"): a man beats another man to death for no particular reason. The latter is punched in the face and repeatedly punched after he's on the floor. Two other men watch in horror. The man is later dragged away with his face covered in blood.
Season two, episode six ("Peek-a-boo"): a female character hits an ATM machine onto a male character's head. Not very bloody or graphic, but still quite hard to watch because it's very shocking.
Season three, episode one ("No Mas"): Two gunmen in a truck begin to massacre illegal immigrants inside and only gunshots are heard. They emerge from the truck and shoot the fleeing driver. His death is seen from a distance.
Season three, episode three ("I.F.T"): in the first five minutes of the episode, someone's head is chopped off with a machete. Very brief but could be quite disturbing to some viewers. The decapitation is shown off screen, but we see a streak of blood hit a wall. The head is later seen on a turtle shell.
Season three, episode seven ("Sunset"): in the prologue before the theme song starts, a policeman is killed by an ax and an elderly woman's corpse is shown.
Season three, episode eight ("One Minute"): in the end, a shootout happens at a parking lot. An innocent bystander is shot and killed, one gunman is critically wounded and the other is shot in the head. Brain matter splatters over the camera.
Season three, episode 13 ("Full Measure"): a man points his gun at a wall (another man's head is on the other side), and shoots. A moderate amount of blood splatter can be seen from a distance.
Season four, episode one ("Box Cutter"): a man's throat is suddenly sliced with a box cutter. Very bloody and extremely shocking. The body is later dissolved in acid.
Season four, episode 13 ("Face Off"): a bomb goes off in a room with three people inside. One man walks out, still alive. The camera then rotates to show that half of his face has been blown off. (This is rather graphic and disturbing, but only last about 5 seconds) He then falls face first to the camera and dies. This is reminiscent of "Two-Face" in The Dark Knight but much more graphic and disturbing.
Season five, episode eight ("Gliding Over All"): 10 people are killed in a two-minute jail montage. They are stabbed, beaten, and burnt to death. There isn't a great amount of blood, but the overall acts of violence are strong and disturbing.
Season five, episode sixteen ("Felina"): At least ten people are shot by a machine gun with some blood spraying onto walls. A man is strangled to death by a chain; this lasts for about 15 seconds, and we see the man who's getting strangled struggle on the floor and we hear his neck snap. A man who is coughing up blood after being shot in the stomach is shot in the head. Blood splatters onto the camera lens as we see this from his perspective.
NOTE: Breaking Bad is a sometimes difficult show to determine the appropriate age range for, as most episodes (i.e. "Phoenix," "Fly") will go by with very little violence, but there are infrequent instances of bloody, extremely realistic violence. Violence is not glorified on this show, and some characters have trouble dealing with their violent actions, but it can still be disturbing. (Ex. A man is forced to kill a man he knows and is seen crying while holding him at gunpoint)