In cellular wireless networks, user association refers to the problem of assigning mobile users to base station cells - a critical, but challenging, problem in many emerging small cell and heterogeneous networks. This paper considers a general class of utility maximization problems for joint optimization of mobile user associations and bandwidth and power allocations. The formulation can incorporate a large class of network topologies, interference models, SNR-to-rate mappings and network constraints. In addition, the model can applied in carrier aggregation scenarios where mobiles can be served by multiple cells simultaneously. While the problem is non-convex, our main contribution shows that the optimization admits a separable dual decomposition. This property enables fast computation of upper bounds on the utility as well as an efficient, distributed implementation for approximate local optimization via augmented Lagrangian techniques. Simulations are presented in heterogeneous networks with mixtures of macro and picocells. We demonstrate significant value of the proposed methods in scenarios with variable backhaul capacity in the femtocell links and in cases where the user density is sufficiently low that lightly-used cells can reduce power.