You have several method but they don't work for all model... it is mainly related to the level of detail from the model...
First, you can work with automatic tools... by example, i use the BlackSmith3D suite... but it is not perfect... take a look at the dragon picture at http://www.blacksmith3d.com/blacksmith3D-3d-modeling-software.php ... poly reduction is working but the result have a lot of multi side poly... once triangulate again, the reduction is really minimal...
Manually, you can delete some edges on big flat surface, check if you have not double eges, isolated vertice... in some case, it is beneficial to cut a object in two... by example, for a little cube extruded from a big one, the junction is 8 tri... if you separate them in two object, two new face will be 2 tri each...
Like xXx explain, for some more complex piece, who eat a lot of poly, it is better to remodel these piece... will be more fast...
In some case, it is almost impossible to reduce poly... by example, you will have difficulty for reduce the poly from my own model since i apply all the trick that i know for have already a low poly count when i create the model... only way will be that you know a trick that i don't know...
In short, it is possible... but it is mainly a manual work and related to the model itself...