In Buddhism, 'sutra' (Sanskrit) or 'sutta' (Pali) refers to canonical scriptures that are believed to be based on actual oral teachings of the Buddha. Although none of them were written down during his lifetime, tradition teaches that his senior disciples memorized his major teachings, and recited all of them soon after his death. Initially, these were passed from teacher to student between generations orally, but eventually they were written down. Over the centuries, as Buddhism migrated throughout the Far East, slightly different collections and translations evolved, but the core sutta contents of the Pali Canon are consistent, and are generally acknowledged as canonical amongst all branches of Buddhism.
Mahayana Buddhism, of which Tibetan, Chinese and Zen Buddhism are all a part, has an additional set of sutras, that they believe are also based on direct teachings of the Buddha (note that often 'sutra' is used to refer to these collections, while 'sutta' is used to refer to the Pali Canon, although depending on the context, the spellings might also be used interchangeably.) However, Theravada Buddhists do not recognize these sutras as deriving from the Buddha, believing them to be later compositions.
Below is a partial list of the major categories of sutras/suttas found within each tradition, as well as some of the most well-known in each category. Over time, overviews of the major sutras/suttas will be linked to from here.
Major Collections ('Nikayas') in the Sutta Pitaka, Pali Canon
Digha Nikaya: Called the 'long' discourses, there are 34 suttas in this collection. Some of the most well-known are the Maha-parinibbana Sutta, which describes the end of the Buddha's life, the Brahmajala Sutta, which compares the Buddha's teachings with other ascetics of India at the time, and the Potthapada, which describes the benefits of samatha meditation.
Majjhima Nikaya: Called the 'middle-length' discoures, there are 152 suttas in this collection. Among other topics it includes shorter discussions on karma, mindfulness, and breathing.
Samyutta Nikaya: This includes thousands of 'short' discourses, on virtually every topic. The exact number is unclear, because different translations group them differently.
Anguttara Nikaya: Another grouping of thousands of short suttas. One of the better known is the Kalama sutta, or 'discourse on free inquiry', in which the Buddha exhorts practitioners to follow only what they have verified for themselves.
Khuddaka Nikaya: This collection is a mix of talks, stories, and poetry from both the Buddha and some of this direct disciples. One of the most well-known and oft-translated suttas, the Dhammapada, is part of this collection, as is the Therigatha or 'Verses of the Elder Nuns', one of the few collections of early Buddhist writings attributed to women.
There is more variation between Mahayana traditions in terms of which sutras are canonical, but here are some primary ones.
The Heart or 'Heart of Perfect Wisdom' Sutra: One of the sutras included in the Prajnaparamita or 'Perfection of Wisdom' collection, which is recognized by most Mahayana schools. The Heart Sutra describes the enlightenment of Avalokitsvara, the bodhisattva of compassion, through the attainment of 'prajna' (wisdom) gained through meditation on the emptiness of all phenomena.
The Diamond Sutra: Also part of the Prajnaparamita, this sutra focuses on avoiding the extremes of attachment, both emotional and mental, particularly to fixed concepts and ideas.
The Lotus Sutra: This sutra is one of the first to use the term 'Mahayana' or 'great vehicle', and to refer to the Buddha as an eternal teacher of eternal teachings. It contains many parables concerned with 'skillful means' and is also one of the first to state that anyone can become a Buddha. (For Thich Nhat Hanh's take on this sutra, see my review of his book Peaceful Action, Open Heart.)
Mahaparinirvana Sutra: This sutra uses events from the final months and days of the Buddha's life, and his passing, as a means for relaying teachings. It is known for its supernatural stories and ideas.
Other major Mahayana sutras include Brahmajala (Ten Grand Precepts), Buddhavatamsaka (the Flower Garland), Shurangama (Heroic Gate), Ratnakuta (Jewel Heap), and Ananta-nirdesa (Innumerable Meanings).
Try the following two books for introductions to the Pali Canon and Mahayana Sutras respectively: In the Buddha's Words -Bhikkhu Bodhi and Mahayana Buddhism - Paul Williams