Do noise-cancelling headphones make a lot of unheard noise? The way noise cancelling headphones work is by listening to sound, and created the inverted sound to 'cancel it out'. Doesn't this mean that the headphones create double the amount of noise, but our ears just can't pick it up due to the noise being 'equalized'?
 A: This question blends over into the realm of Physics:
Yes, noise-cancelling headphones create what is known as 'anti-sound', which is (virtually) the same sound (and equally loud) as can be heard in the environment, but with an inverted phase.
This inverted sound wave indeed cancels out the original sound wave from the environment, resulting in (virtually) no air displacement at your ears: i.e. no sound, no noise.
The actual anti-sound created by real-world noise-cancelling headphones is not exactly the inverse sound as your surroundings, but a (close) approximation. The quality of this approximation limited by the quality and latency of the microphones, chip, software and speakers in the headphones. This means that they will only reduce and not perfectly cancel all noise.
It also means that if you have a noise that only lasts a very short time, the headphones might actually be too slow to cancel the noise. In this case, your ears will first hear the original sound (at full volume) and then the anti-sound (also at full volume). In this case you could say that the headphones have created a lot of additional noise (which in that case will be heard).

To summarize: Yes, noise-cancelling headphones are constantly making noise themselves. The net effect of this is however that the amount of noise that reaches your ears is greatly reduced.
A: Well, Qqwy, has provided a nice answer to you, so I am just gonna try to add up to that.
As has already been mentioned, the actual realization of an active noise cancellation device has many implications. Latency being just one of them (more of them include imperfections in modelling, the transfer function of the components, incorrect equalization and a whole bunch more).
One thing to keep in mind though is that if the source and "cancelling device" are not co-located (i.e. they do not occupy the exact same space) you cannot completely cancel the generated sound field in the whole domain of interest. This means that when the two sources' (original source and cancelling source) locations start to depart from each other you will start to have "artefacts" from the existence of the second (cancelling) source.
Some well-known techniques (used extensively in active noise control in headphones) include the cancellation of noise at a specific point in space. Keep in mind though that this, almost for sure (especially true for broadband sounds), will increase the sound pressure level in some other point in space. A different approach is concerned with the minimization of the noise power, which does not necessarily coincide with complete cancellation of the noise in a specific point or direction.
Now, regarding the specifics of noise-cancelling headphones, one has to also take into account the fact that the headphones themselves affect the sound field and due to diffraction, as well as other phenomena which become increasingly important in this scale (such as the viscosity close to the boundaries of both the headphone and the ear, the heat variations in case of "muffle-like" headphones and a lot more), which are very difficult to anticipate/foresee, the effectiveness of those devices/techniques can be very easily compromised.
Additionally, you have to keep in mind that this technology is effective primarily at low frequencies because in the "high-frequency regime" small variations in space can result in big variations in pressure, so any small imperfection of the equipment (or conditions) can result in doubling the pressure instead of cancelling it.
I apologize for not providing any in-text references, but those interested can find condensed information from this an article by Elliot and Nelson titled Active Noise Control, IEEE Signal Process. Mag., October, or books like Active Control of Sound by Nelson and Active Control of Noise and Vibration by Hansen et al.
