We study quantum trajectories of collective atomic spin states of N effective two-level atoms driven with laser and cavity fields. We show that interesting “entangled-state cycles” arise probabilistically when the (Raman) transition rates between the two atomic levels are set equal. For odd (even) N, there are (N + 1)/2 (N/2) possible cycles. During each cycle the N-qubit state switches, with each cavity photon emission, between the states (|N/2, mi ± |N/2, −mi)/ √ 2, where |N/2, mi is a Dicke state in a rotated collective basis. The quantum number m (> 0), which distinguishes the particular cycle, is determined by the photon counting record and varies randomly from one trajectory to the next. For even N it is also possible, under the same conditions, to prepare probabilistically (but in steady state) the Dicke state |N/2, 0i, i.e., an N-qubit state with N/2 excitations, which is of particular interest in the context of multipartite entanglement.