Here is a selection of some really important Pali Suttas. Deep bows to accesstoinsight.org.

First is:
Kalama sutta - to the Kalamas
which gives the Buddha's recommendation as to the attitude one should take towards the teachings.

Then the 1st, 2nd and 3rd discourses:

1st Discourse - Setting the Wheel of Truth in Motion

Anatta-lakkhana Sutta - The Characteristics of Non-Self

Adittapariyaya Sutta - The Fire Sermon

The heart of the matter, dependent origination:
Paticca Samuppada - Dependent Origination

The Simile of the Saw - Kakacupama

The subtle understanding of the 'self':
Ananda Sutta -To Ananda (On Self, No Self, and Not-self)

Magga-vibhanga Sutta - Analysis of the Path

How to do it:
Maha-satipatthana Sutta - The Foundations of Mindfulness


Here are links to suttas I find particularly inspiring:

Bahiya Sutta - About Bahiya

Bhaddekaratta Sutta - An Auspicious Day

Kamada Sutta - Kamada's Lament

Lokavipatti - the 8 Worldly Conditions

Udayi Sutta - Hard to teach the Dharma

Chiggala Sutta - Blind Sea Turtle and the Hole

Vaca Sutta - Right Speech