Let $C/K$ be a curve of genus > 2 over a number field $K$ and suppose there exists a $p \in C(K)$. Then a recurring theme in studying $C(K)$ is using the map $C \to J(C)$ normalized by sending $p$ to 0, for example Faltings proof that $C(K)$ is finite, Chabauty-Coleman, Mazurs determination of all $\mathbb Q$ rational points on $X_0(N)$.

I want to know if there are also techniques for studying $C(K)$ that don't use the Jacobian.

My main motivation is that I later want to explicitly apply these techniques to a curve $C/\mathbb Q$ for which I can prove that the closure of $J(\mathbb Q)$ is of finite index in $J(\mathbb Q_p)$ for all primes p so that Coleman-Chabauty does not work. The techniques don't necessarily need to fit in a nice theoretical framework, examples in the literature where rational point questions on specific curves are solved without using their Jacobian are welcome to!

One example that I know of is Runge's method which was recently succesfully used to study rational points on certain modular curves by Bilu and Parent http://arxiv.org/abs/0907.3306