On Buddhist pessimism:

Buddhism never was a pessimistic religion. In fact, it encouraged and pursued happiness in a realistic manner like no other religion had, or did, afterwards. But, the Buddha encouraged long-term gratification over short-term gratification. He did not mean to make people contemplate on the sad things in life, but wanted them to realize that happy and sad things were equally fleeting and impermanent. Therefore, He wanted them to take a "middle path" which was as detached from the sad things as much as from the happy things. Stressing the importance of the mind and intelligence ("Buddhism is not a religion for fools, but for the wise"), He wanted us to know that all feelings were a concept of the mind. If not so, He argued, the same act of sitting down, which is considered a comfort at the beginning, cannot become a discomfort after being seated continuously for three consecutive days. The act has remained the same. What has changed is the perception it creates in our minds.
Likewise, all feelings can be conditioned by our minds to be whatever they want to be. But, the Buddha wanted us to be more realistic and courageous than that. He wanted us to perceive feelings as painful, or pleasing, or as neither but in-between. And thus perceiving feelings, to take them as they are, and not be disappointed and discouraged, nor elated. This meant that one does not have to go in pursuit of happiness or be taking pains to avoid sad events, because both types of events are inevitable in one's life. If one wants to avoid sad events from taking place permanently, one needs to end one's unceasing cycle of lives by practicing "The Noble Eight-Fold Path". Now, this eight-fold path is not something that can be successfully pursued by Buddhists only, but by any person who does so willingly. What is important to note here is that He did not say that people who do not believe in Him are going to be eternally damned, but that one does not have to believe in a Buddha or in Buddhism to gain salvation. "Salvation" is not a very appropriate term to be used in a Buddhist context because it implies the gain of a thing that the Buddha promises not. But then again, the Buddha does not promise anything.
What He did say was that if you use your head wisely, you will be free and happy. If you do not, and measure your happiness by worldly things and cling to them blindly, you will never find true and supreme happiness. Isn't it wonderful to know that you don't have to be rich, nor powerful, nor beautiful to be happy?
Is Buddhism fatalistic (and encourage apathy)?
These are sayings in Buddhism that I've found to be inspiring, and are selfishly collected here for personal reference.
" Not to do any evil, to cultivate good, to purify one's mind, this is the Teaching of the Buddhas.
" Gauging others as one's equal, superior, or inferior is itself a form of ignorance.
" He for whom there exists neither this shore nor the other, nor both, he who is undistressed and unbound, him I call a brahman (a person of high birth).
" All conditioned things are impermanent. When one sees this in wisdom, then he becomes dispassionate towards the painful. This is the path to purity.
" He who holds back arisen anger as one checks a whirling chariot, him I call a charioteer; other folk only hold the reins.
" He who has transcended both merit (good) and demerit (evil), he who leads a pure life, he who lives with understanding in this world, he, indeed, is called a bhikku (a monk).
" By degrees, little by little, from moment to moment, a wise man removes his own impurities, as a smith removes the dross of silver.
" He who, seeking his own happiness, torments with the rod creatures that are desirous of happiness, shall not obtain happines hereafter.
" The most excellent ascetic practice is patience and forbearance. Nibbana is supreme, says the Buddhas. He indeed is no recluse who harms another; nor is he an ascetic who hurts others.
" To speak no ill, to do no harm, to practise restraint according to the fundamental precepts, to be moderate in eating, to live in seclusion, to devote oneself to higher consciousness, this is the Teaching of the Buddhas.
" Happy indeed we live without hate among the hateful. We live free from hate amidst hateful men.
" The conqueror begets enemity; the defeated lie down in distress. The peaceful rest in happiness, giving up both victory and defeat.
" Having tasted of the flavor of solitude and tranquility, one becomes woeless and stainless, drinking the essence of the joy of Truth.
" As a solid rock is not shaken by the wind, even so the wise are not ruffled by praise or blame.
" Happy in this world is non-attachment.
" This body of flesh and blood I bear, all for the world's good and welfare.
" By self is one defiled, by self is one purified.