The editing history is always available to someone who looks for it (by clicking on the "edited [time]" at the end of an edited answer), so your question is: Should we make the edit history explicit in the answer itself?
My answer is No. Simply folding the edits appropriately into the answer makes for less clutter, and a better, concise answer. This is useful to everyone, both the original questioner and those who arrive at the question in the long term, and (to borrow Juan's phrase) "people just don't want to read the whole saga of how the answer was improved over time". (Disclaimer: This here is a remark about hypothetical excesses of historiography, not about the fine answer that provoked the previous thread.)
However, in order to be fair, it's good to briefly mention your edit whenever (1) you borrow or steal from another answer — so that it doesn't seem the other answer was redundant, and to give credit, or when (2) you edit the question to invalidate one of the answers previously posted — so that their answer doesn't seem unduly inapt. Most edits are not of this form, though, and I feel that when they are, a brief but clear mention of the change suffices.
Andrew suggests it's better to preserve edit history by marking off edits separately, "since that person knows what I originally wrote and is only interested in seeing what has been added". This is a nice idea, but I'm unconvinced. Whom does it help? Someone who
- reads the answer in the interval after it was originally posted and before it was edited, and
- visits the thread again after the edit, and looks at this particular answer, and
- remembers what was written and doesn't want to reread it, but
- knows to look for "Edit" to see what's new.
Not very frequent, in my view. Certainly, you must mark edits when you make a major change, something that may easily be missed by a reader of the previous text and which is substantial and important enough that a previous reader's attention ought to be drawn to the new material with a bold "Edit" (e.g. you remove something bad, or when your original answer was so long that it won't be reread unless you draw attention). But in most cases, this is not necessary, and even when this happens it's good to eventually go back and clean up the answer to remove 'history clutter'. (Also, when the changes introduced in the edits are logically distinct from the previous, it's better to eventually use descriptive titles like "Explanation" or "Caveat" rather than "Edit" and "Second Edit".)