Three manifold groups are quite special and their representation varieties have more structure than that of a random group. Casson's view point is helpful to see the point. The Heegaard decompoistion of a three manifold $Y= H_1\cup_\Sigma H_2$ means that the fundamental group of a three manifold has a quite special presentation. There is pushout diagram, \begin{eqnarray} \pi_1(\Sigma) & \to & \pi_1(H_1)\\ \downarrow & & \downarrow \\ \pi_1(H_2) & \to & \pi_1(Y) \end{eqnarray} and hence maps in the opposite direction on representation varieties.
\begin{eqnarray}
R_G(\Sigma) & \leftarrow & R_G(H_1)\\
\uparrow & & \uparrow \\
R_G(H_2) & \leftarrow & R_G(Y)
\end{eqnarray}
The representation variety $R_G(\Sigma)$ is a symplectic manifold when $G$ is compact Lie group (thanks to Goldman and Atiyah-Bott) and gets a Kahler structure
once metric is chosen on Sigma$\Sigma$. If $G$ is the complexification of a compact Lie group and a metric on $\Sigma$ is choose $R_G(\Sigma)$ is Hyperkahler manifold.
(It is a slight lie (small l ;-) that these are manifolds.)
The maps $R_G(H_i) \to R_G(\Sigma)$ are injective and images (to the extent they are manifolds) are Lagrangian in case $G$ is compact and complex Lagrangian when $G$ is the complexification of a compact group. The intersection
$$
R_G(Y)=R_G(H_1)\cap R_G(H_2) \subset R_G(\Sigma)
$$
is then much more special, so in the compact case lies in the setting of Lagrangian Floer homology and the in the complex case in the setting is for example discussed recently by Witten and Haydys (see for example arXiv: 1010.2353 )
Related to this point of view is the fact that representation varieties of three manifolds are the set of critical points of a Chern-Simons functional on a suitable space of gauge equivalence classes of connections.
Apologies for the inaccuracies above due to haste and lazy typesetting.