This paper presents distributed conjugate gradient algorithms for distributed parameter estimation and spectrum estimation over wireless sensor networks. In particular, distributed conventional conjugate gradient (CCG) and modified conjugate gradient (MCG) are considered, together with incremental and diffusion adaptive solutions. The distributed CCG and MCG algorithms have an improved performance in terms of mean square error as compared with least--mean square (LMS)--based algorithms and a performance that is close to recursive least--squares (RLS) algorithms. In comparison with existing centralized or distributed estimation strategies, key features of the proposed algorithms are: 1) more accurate estimates and faster convergence speed can be obtained; 2) the design of preconditioners for CG algorithms, which have the ability to improve the performance of the proposed CG algorithms is presented and 3) the proposed algorithms are implemented in the area of distributed parameter estimation and spectrum estimation. The performance of the proposed algorithms for distributed estimation is illustrated via simulations and the resulting algorithms are distributed, cooperative and able to respond in real time to change in the environment.