Stimulated emission and No cloning theorem
Sure you can clone a state. If you know how to produce it, you can just produce one more copy.
The answer to your question therefore lies in the specifics of the no-cloning theorem. It states that it is not possible to build a machine that clones an arbitrary (previously unknown!) state faithfully.
Stimulated emission does not fulfill this. Given an atom, only a certain range of frequencies, etc. can actually be used to produce stimulated emission, so you can't faithfully clone an arbitrary state. It's just an approximation to cloning, which is not prohibited.
See also: http://arxiv.org/abs/quant-ph/0205149 and references therein.
In stimulated emission the field starts in a state containing $n$ photons, and ends up in a state containing $n+1$ photons. The system has made a transition from one state to another. It looks to me like nothing has been cloned. Same system, different states.
I think @garyp has given the correct answer, but it is worth expanding on it a bit.
Stimulated emission is not cloning a state, but rather changes the state of a mode (characterized by wavelength, direction, polarization, etc.): $$ |n_{\mathbf{k},\lambda}\rangle \longrightarrow |n_{\mathbf{k},\lambda}+1\rangle . $$
The conceptual misunderstanding here is due to the possible lack of background in quantum field theory, and therefore thinking of photons as if they were particles. This leads to thinking that a new photon is another particle in a state identical to the states of the previous ones. Once it is understood that photon is not a particle (not in the first quantization sense at least), but a level of excitation of a single mode, the contradiction disappears.
The most direct "particle" parallel is an electron in a harmonic potential, changing its state from $n$ to $n+1$ - the two states are not identical, even though the potential frequency is the same for them.
Update
Perhaps an explanation is needed why no-cloning theorem does not appear in my answer. Word cloning in its most generic sense means producing two identical copies of something (cloning is just a buzz word for copying, duplicating). Thus, my answer could be summarized as stimulated emission is not cloning (in any sense of this word). This is a more general statement than saying that stimulated emission is not equivalent to a specific type of cloning in the domain of physics, e.g., such as implied by the no-cloning theorem.
Implementing no-cloning theorem would require that we have two identical systems which then could be excited into the same state. I.e., we could have two identical lasers (laser A and laser B) initially in different states and then synchronize them: $$ |n_{\mathbf{k},\lambda}\rangle_A \otimes |m_{\mathbf{q},\mu}\rangle_B \longrightarrow |n_{\mathbf{k},\lambda}\rangle_A \otimes |n_{\mathbf{k},\lambda}\rangle_B. $$ We could also define cloning af two modes (but not the whole systems) being in identical state: $$ |n_{\mathbf{k},\lambda}\rangle_A \otimes |m_{\mathbf{q},\mu}\rangle_B \longrightarrow |n_{\mathbf{k},\lambda}\rangle_A \otimes |m_{\mathbf{q},\mu},n_{\mathbf{k},\lambda}\rangle_B. $$ We could even concievably talking about cloning some of the photons to the corresponding mode of the other laser $$ |n_{\mathbf{k},\lambda}\rangle_A \otimes |m_{\mathbf{q},\mu}\rangle_B \longrightarrow |n_{\mathbf{k},\lambda}\rangle_A \otimes |m_{\mathbf{q},\mu},l_{\mathbf{k},\lambda}\rangle_B. $$
In other words, there are many things that one could conceivably call $cloning*, but the term is hardly applicable to the "identical" photons, since they are not really different entities that could be identical, but rather different states of the same system.