In The Force Awakens, we see a rogue stormtrooper. This could be explained as a "glitch in the code" and many may have passed it by, but then he says something about being taken away from his family - which is a bit odd, if they were a clone, unless they were given fake families which I highly doubt. This made me wonder if the Empire have stopped using the clones for their storm troopers, and if this is the case, why?
All the stormtroopers we see in the TFA canon so far are not clones.
We know that they could use clones if they wanted to.
We do NOT have any proof that they do not use clones in general.
There reasons for not using clones:
Current army heads don't like the idea, because of either valid military reasons, or military-theoretical dogmatism.
We do NOT know if they are using clones in general with absolute certainty.
We DO know that:
They are not using clones as stormtroopers reporting specifically to General Hux (since he appears to be top Army commander for First Order, presumably they either don't use clones at all because he'd object, OR, they don't use them widely).
They can use clones, or at the very least, Kylo Ren thinks so.
This comes from the following info:
Exchange betwen Hux and Ren (source: TFA novelization by Alan Dean Foster):
Ren paused to consider the general’s words. “A simple enough task, or so it would seem. Find one droid. Just how capable are your soldiers, General?”
Hux turned away from the trooper’s holofile. He respected Ren and his abilities, but he was not afraid of him. One did not rise to the rank of general in the forces of the First Order by showing fear. “I won’t have you questioning my methods.” “What methods would those be, General? Those that allow a single common trooper to free an important prisoner from confinement, escort him to an operating hangar, and assist him in fighting his way to freedom? What methods teach such expertise? Obviously, at least some of your troops are skilled at high treason. Perhaps Leader Snoke should consider using an army of clones.”
It was with great difficulty that Hux restrained himself. “My men receive exceptional instruction. They are programmed from birth to be loyal to one another, to their officers, and to the Order. The appearance of a single abnormality does not give you the right to question methods that have been refined through long—”
Finn's statement that he was taken from his parents as a small child.
Visual Dictionary by Pablo Hidalgo, Hux and Phasma pages.
It intimates that Hux is one of the top commanders in the FO military, though doesn't say so very clearly and definitely hard to tell if he's THE top commander or just one of many generals commanding a portion of the army.
It also talks extensively about Hux's training philosophy origin (real soldiers, trained special way); as well as Phasma's dislike of old stormtroopers who in her opinion were ineffective.
According John Boyega in Rolling Stone magazine’s web piece filled with tidbits they did not include in their main “behind-the-scenes” story on The Force Awakens:
There are no clones left in the ranks of Stormtroopers – which is why John Boyega is under one of the helmets, rather than the guy who played Jango Fett in the prequels
“They’re not using clones anymore,” says Boyega, “and that is all cleared up in the film. It’s not that deep!”
The first time the clones saw action (episode 2, IIRC), they were capable of taking out Jedi.
Chronologically later, in episode 4, these clones could not hit the broad side of a barn, and in episode 6 a legion of the best of them got whupped by some living teddy bears.
Clearly, the quality of clones went into such rapid decline that by the time episode 7 takes place, clones can barely dress themselves without accidentally shooting a squad mate, and only a fool would make use of them.
It is possible, however, that the First Order is utilizing GeNode clones, which were in use during the Galactic Empire (40% of the Imperial Army around the time of the Battle of Endor, I believe), and were also used during the Galactic Republic (Though not nearly as many). GeNode clones are bred with false memories and the belief that they are not, in fact, clones. They fit the description for even a character such as Finn (FN-2187), as he claims to have been "Taken from his family at a very young age". Just a theory, however. I advise anyone interested to look into Wookieepedia's article on GeNode clones.