As I understand lasers, you start off with a few photons that are in an identical state, and other photons that are created later tend to have the same quantum numbers due to Einstein-Bose statistics. Isn't each photon that "joins" the group of preexisting ones a clone of the previous ones? Why doesn't this violate the no-cloning theorem?
As Rococo already pointed out, the no-cloning theorem doesn't forbid cloning of all specific states. It just states that you cannot make copies of arbitrary (general) states.
Let me (briefly) reiterate the core of the theorem: To clone a state you need a linear operator C that maps a state $|a\rangle|0\rangle$ to $|a\rangle|a\rangle$. This is not possible for general states: $$C |\lambda a+ \mu b\rangle|0\rangle$$ would have to map to $$|\lambda a+\mu b\rangle|\lambda a+ \mu b\rangle$$ per definition of the operator. But linearity (and homogenity) leads to $$C |\lambda a+\mu b\rangle|0\rangle = \lambda C|a\rangle|0\rangle + \mu C|b\rangle|0\rangle = \lambda|a\rangle|a\rangle + \mu |b\rangle|b\rangle$$ while $$ |\lambda a+ \mu b\rangle|\lambda a+ \mu b\rangle = \lambda^2|a\rangle|a\rangle +\lambda \mu (|a\rangle|b\rangle+|b\rangle|a\rangle)+\mu^2|b\rangle|b\rangle$$
So you see that for e.g. $\lambda=1, \mu=0$ (i.e. a base state) there is no contradiction. But you can't clone a general superposition of your base states.
A short history of the laser:
1917: Einstein describes theory of stimulated emission
Following decades: Lasers (and masers) are thought to be impossible due to quantum theory (Everyone knows Einstein was wrong about quantum theory :)
1951 Charles Townes builds a maser - some people are just awkward (John von Neumann: 'That can't be right', Niels Bohr: 'But that is not possible' - see How the Laser Happened: Adventures of a Scientist)
1982 Nick Herbert invents FLASH - A superluminal communicator based upon a new kind of quantum measurement (see How the hippies saved physics : science, counterculture, and the quantum revival )
Later in 1982: No-cloning theorem is devised, explaining why FLASH won't work.
So how was FLASH supposed to work? Well two entangled photons were produced with the "same" polarization (Actually, I think, they will be opposite polarizations, but that can be dealt with, and I'll ignore it from now on) One of the photons is measured at one place, thus collapsing the wave function. At another place the other photon is fed into a laser, which produces lots of photons with the "same" polarization. Measuring several of these allows you to work out how the wave function has collapsed, and thus what measurement was made at the other location, allowing superluminal information transfer.
The trouble is that, in reality the word "same" has two different meanings. In the entanglement case it means that the result will be the same whatever polarization measurement you do. In the case of the laser it doesn't - as wataya says, it might clone the linear polarization, but not the circular polarization.
I think there is a problem here, but I'm not sure what it is. It may be our ideas of quantum states - saying two states are both represented by |H> doesn't actually tell you how much the same they are. Or it could be our ideas of lasers - that the common idea of one photon stimulation the emission of another is inaccurate, and that the working of lasers has to be thought of as a collective way.