The Rambam (Rabbi Moshe Maimonides, Spain-Egypt, 1135-1204), in the first chapter of his Hilchot Teshuva (listen to audio for precise citation), identifies four categories of sin with respect to the necessary means of achieving atonement:
1) One who neglects to perform a Misvat Ase, one of the Torah's affirmative commands, earns atonement immediately upon his performance of Teshuva (repentance). Thus, for example, if a person does not take a Lulav or sit in the Sukka on Sukkot, once he confesses and sincerely repents for his wrongdoing, his sin is atoned.
2) The second category consists of standard Misvot Lo Ta'aseh Torah prohibitions that are not punishable by Mitat Bet Din (court execution) or Karet (eternal excision from the Jewish people). Sins in this category, such as wearing clothes containing Shaatnez (a combination of wool and linen), are atoned through repentance and the observance of Yom Kippur.
3) For prohibitions that carry a punishment of Mitat Bet Din or Karet, one does not earn complete atonement by performing Teshuva and observing Yom Kippur. Atonement is possible for these transgressions only by enduring Yisurim suffering, Heaven forbid in addition to Teshuva and the Yom Kippur observance. One example of this category of sin is Shabbat desecration.
4) The Rambam concludes by noting that if one created a Hillul Hashem desecration of God's Name such as if he committed a sin publicly then he cannot achieve complete atonement until death, Heaven forbid. Even after repentance, Yom Kippur, and suffering, a sin of Hillul Hashem, given its particularly grievous nature, is not fully erased until the violator dies.
