Many of scholars , buddhists and non-buddhist alike, have helped in propagating the idea that the main teaching in Buddhism are about the Law of Kamma (do good receive good, do bad receive bad) and reincarnation. This is very wrong and ought to be corrected.
The teaching about the law of kamma (LOK) and reincarnation existed before the Buddha's time. The Buddha did not deny the essence of the LOK but added to it that there is another kamma (action) which is neither GOOD nor BAD. This kamma is BEYOND good and bad. This is the kamma that will enable the aspirant to live BEYOND the effect of the law of kamma. The Buddha had added a major chapter to and COMPLETED the law of kamma.
To be good is not good enough; one needs to transcend even the good quality. Bad effect of kamma is suffering (Dukkha). Good effect is also suffering (but people like us don't see it as such.) The third form of kamma is the kamma that will end the effect of kamma (i.e. , suffering) It's the END OF SUFFERINGS which is not the same as HAPPINESS. But we often call it 'happiness' (in order to be 'spiritually/psychologically correct.')
As to reincarnation, the most lofty teaching of the Buddha is about Not-self/Emptiness (Anatta/Sunyata). When there is no self/soul to be reborn, who, then, reincarnate? The theory of reincarnation is thus contradictory to the main teaching of the Buddha. The reasons behind its inclusion in many Buddhist scripts are long and complex and practitioners need not waste their precious time and energy to find out.
Note that the Buddha did not deny the reincarnation theory. He did not base his teaching on it because it's irrelavant to the practice at the PRESENT MOMENT. The practice at the present moment to liberate oneself from the sufferings does not and cannot depend on the existence of the future lives. If one does rightly at the present moment the next moment would also be right and so on so forth; the next life, if existed at all, would also be right automatically. Practitioners ought to concentrate their energy to the practice at the present moment instead of diluting it in thinking about the next reincarnation. As Than Buddhadasa often said: "Even this life does not exist, how could the next life exit?"
If there is no self, who attains enlightenment? This ancient (and still popular question) can be answered simply as: Enlightenment does not exist; how could a self, even if existed, attain enligthenment? We obviously have a semantic problem. The concept of differentiating between the people language and the Dhamma language as proposed by Buddhadasa Bhikkhu is very helpful in this respect. As he also often said: "Be liberated from the liberation!" If I may add: True Enlightenment can be attianed only if there is no-one to attain it! Many of the weird and incompatible saying in Buddhism can be resolved if we know how to separate dhamma language from people language.
Some people would also like to reduce Buddhism to mere code of ethics. Most of the buddhist code of ethics existed before the Buddha's time. The Buddha even allowed them to be modified in the future, to be appropriate to time and places. We could very well say that the universal code of ethics as wise people of each time and places had proposed for people to live together peacfully , such as universal love and compassion, is good enough to be the Buddhist code of ethics. Even the ethics that are related to non-attachment are not purely Buddhistic for the concept of non-attachment also existed before the Buddha's time (albeit, not right enough or complete enough).
If Buddhism is mere code of ethics then we need no Buddha. The main teaching in Buddhism always are: the third, not good, not bad kamma and the doctrine of no self/no soul. Both of these teachings are compatible with the the teaching of non-attachment. Suffering is caused by attachements to the five aggregates of existence which manifest themselves in the forms of the concept of good-bad duality and the concept of self/soul (or Self/Soul).
Buddhism is not a philosophy. Philosophy is based on speculations of untrained minds and it does not offer any form of spiritual salvation. Buddhism is an art of living at the present moment: to live a life as free from suffering, gross and subtle, as much as possible. The ultimate, permanent freedom from sufferings is the buddhist's salvation.
All the above is inspired by the teaching of Buddhadasa Bhikkhu ( 2449-2536 B.E., 1906-1993 A.D.), a Thai monk who spent most of his life reforming/restoring Buddhism.
Enlightenment cannot be obtained by various strange systems of morality or strange conducts, but by the wisdom to see and to uproot the cause of suffering. -- Buddha (translated and paraphrased)