In order to get the relative consistency of some statement, it suffices to find a notion of forcing, and a condition $p$ in that forcing, such that $p$ forces the desired statement. It seems to be the case, most often, that the interesting statements we try to force end up being forced by the whole poset.
A sufficient property for a poset to possess to make the above phenomenon occur (in the case where all parameters in the forced statement are canonical names for objects in the ground model) is almost homogeneity: For every $p, q \in P$ there is an automorphism $i$ of $P$ such that $i(p)$ and $q$ are compatible.
It makes sense that if you're building a poset to force something, the whole poset forces it (there's also the ad hoc reason that you could throw out the part that doesn't force it). However, it might happen that in trying to force a particular statement, you build a poset where some, but not all, of the conditions happens to force a different interesting statement. Also, I haven't given this much deep thought, but it seems natural for most posets to be almost homogeneous.
My questions: Are there any interesting, instances of independence results forced by part, but not all, of some poset? Are there examples of commonly encountered posets which aren't almost homogeneous.
(If there ends up being a big list of answers, I'll add the "big-list" tag and make it community wiki)