Is "Bob did what he could in his capability to appease them" a positive or negative comment about Bob?
One person seeks to appease another if the latter has some need and the power to satisfy that need at the former's expense. By appeasing the latter, i.e. satisfying their need, the former can avoid the latter's self-serving behavior and the expense it levies against the former.
Appeasement is often considered the "easy way out" as it's typically quicker, cheaper, and less risky than more aggressive solutions to conflict. This depicts the appeaser as weak, lazy, and/or fearful. Furthermore, when an oppressor dominates a group, a member of the group who appeases the oppressor might even be considered traitorous, as appeasement facilitates (or at least does nothing to resist) the oppressor's actions against the group as a whole and can even be construed as declaration of alliance with the oppressor.
There is nothing positive about appeasement in any scenario, as its very nature implies submission to a destructively dominant and self-interested power. The given phrase, "Bob did what he could ... to appease them," implies (doubly) that Bob is unable to overcome an oppressive force. It suggests Bob is weak, and that he is in a poor position. The situation might not be "serious" (e.g. if "them" refers to his grumpy children), but this phrase certainly does not paint Bob in a positive light.
Edit: I'm referring to literal positivity and negativity. If you're asking whether or not Bob should be insulted to be spoken of in this way... I'd say not. "You're such an appeaser" is a pretty weak insult, IMO.
The term appease itself is fairly neutral:
appease - verb
pacify or placate (someone) by acceding to their demands.
assuage or satisfy (a demand or a feeling).
It's not defined as being disparaging, and you can use it fairly neutrally.
I appeased my growling stomach by eating a sandwich.
We appeased the opposing parties, by throwing some concessions in.
However, it does have some negative connotations, going back to pre-World War II, where Britain's policy toward Hitler under Neville Chamberlain was one of appeasement.
This has been heavily criticised as allowing Hitler to gain momentum and power, and World War II happening.
See the Wikipedia article on Appeasement for more details.
Appeasement as a national policy got negative connotation during WWII:
"The term is most often applied to the foreign policy of the British Prime Minister Neville Chamberlain towards Nazi Germany between 1937 and 1939. His policies of avoiding war with Germany have been the subject of intense debate for seventy years among academics, politicians and diplomats. The historians' assessments have ranged from condemnation for allowing Adolf Hitler's Germany to grow too strong, to the judgment that he had no alternative and acted in Britain's best interests. At the time, these concessions were widely seen as positive, and the Munich Pact concluded on 30 September 1938 among Germany, Britain, France, and Italy prompted Chamberlain to announce that he had secured "peace for our time." (http://en.wikipedia.org/wiki/Appeasement)
Regarding actions of a single human, I'd say the connotations are fairly neutral.
It's "kind of a negative" word.
You know how during a war, when country X is invaded, some people "go along" with the invaders, so as to cause less death, etc? That's "collaborating." So, "even worse" than appeasing, is collaborating - let's say.
I would say that usually -- not always -- appease has a somewhat negative connotation.
It's a bit like speaking about things like ... bureaucracy, government departments, red tape, wishy-washy, flim-flam, dithering.
It is usually but not always, somewhat negative.