Where can I find the law of karma and rebirth in Buddha's own words? Which scripture mentions it explicitly, as told by Buddha, and accepted by all sects of Buddhism?
Ven Bodhi discusses this matter and quotes relevant suttas in his "In the Buddha's Words" chapter V "THE WAY TO A FORTUNATE REBIRTH".
The following list, which was posted on SuttaCentral, is a greatly expanded version of Ven Bodhi's In the Buddha's Words list:
Since i've found Ven. Bodhi reference list, i've been expanding it and here's what it's grown up to thus far. Hopefully someone will find it useful and continue to expand it as one gets more familiar with the Nikayas corpus
The links to the actual texts can be found in this posted list (as a part of a much longer one).
Most (if not all) of the texts are available on Access to Insight as well.
I cannot vouch that the view on kamma presented in these suttas is accepted by all sects of Buddhism, but it at least should be so for Theravada.
The Law of Kamma
(1) Four Kinds of Kamma (AN 4.232)
(2) Why Beings Fare as They Do after Death (MN 41)
(3) Kamma and Its Fruits (MN 135)
(4) Kamma sutta - old and new kamma (SN 35.145)
(5) Sivaka sutta - other causes (SN 36.21)
(6) Devaduta sutta - kamma is only personal (MN 130)
(7) Mahakammavibhanga sutta - the workings of kamma are not simple (MN 136)
(8) Vipaka sutta - violation of 5 precepts leads to states of woe and what they are (AN 8.40)
(9) Tamonata sutta - 4 types of people in the world (AN 4.85)
(10) Saleyyaka sutta/Veranjaka sutta - conduct determines realm of future birth (MN 41/42)
(11) Panatipati sutta (AN 4.214)
(12) Acintita sutta - workings of kamma are incomprehensible and should not be pondered upon (AN 4.77)
(13) Vanijja sutta - success and failure are results of quality of offerings to holy people (AN 4.79)
(14) Dasadhamma sutta - kamma is individual (AN 10.48)
(15) Apayika sutta - false accusers of celibates go to hell (KN : It 48)
(16) Abhinhapaccavekkhintabbathana sutta (Upajjhatthana) - kamma is only personal, everyone is an owner of their actions (AN 5.57)
(17) Acela sutta - on one who experiences the results of kamma (SN 12.17)
(18) Nibbedhika sutta - kamma is intention (AN 6.63)
(19) Angulimala sutta - arahant’s bad kamma gets exhausted in the last life (MN 86)
(20) Lonaphala/Lonakapalla sutta - developed holy way of life alleviates bad kamma; salt simile, jail simile, goat butcher simile (AN 3.99 or 3.100) see (25)
(21) Janussonin sutta - who is born where based on morality (AN 10.177)
(22) Jhana suttas 1,2 - jhana relation to rebirth in heaven (AN 4.123,4)
(23) Metta suttas 1,2 - brahmaviharas relation to rebirth in heaven (AN 4.125,6)
(24) Ariyamagga sutta - 4 types of dark and bright kamma and its results (SN 4.235)
(25) Sankha sutta - bad kamma gets lost in immeasurable brahmaviharas (SN 42.8) see (20)
(26) (Karajakaya) Brahmavihara sutta - bad kamma gets lost in immeasurable brahmaviharas (AN 10.208)
(27) Yodhajiva sutta - warrior which kills is reborn in hell (SN 42.3)
(28) Talaputa sutta - actors are reborn in hell for enhancing asavas in people’s consciousness (SN 42.2)
(29) Sangama sutta 2 - the verse seems to suggest that one’s rewarded with exactly what one has done oneself (SN 3.15)
(30) Samannaphala sutta - sequence of rebirths is linear (DN 2)
(31) Cula-Punnama sutta - where persons of integrity and no integrity end up (MN 110)
(32) Culakammavibhanga sutta (MN 135)
(33) Parikuppa sutta - 5 deeds which lead to hell (AN 5.129)
(34) Sukkhamala sutta - bodily, verbal & mental misconduct lead to hell (AN 3.38)
(35) Ekamsena sutta - bodily, verbal & mental conduct consequences in this life and the next (AN 2.18)
(36) Kukkuravatika sutta - bright, dark, bright & dark, neither dark nor bright types of kamma and its results (MN 57)
(37) Annataro brahmana sutta, Janussoni sutta, Ekamsena sutta - the future is determined by conduct (AN 2.6-8)
Since then I also found these:
Pansu suttas - rebirth in human or deva realms is rare (AN 56.102-113)
Mahasihanada sutta - 5 destinations (MN 12)
Maybe some day someone will volunteer to extract from these suttas relevant excerpts and compose out of them a coherent readily available text.