The Shema is the most central prayer in Jewish life. The first paragraph of the Shema is below (in English!):

Hear O Israel, the Lord is our G-d, the Lord is One.
Blessed is His name, whose glorious kingdom is forever and ever.
Love the Lord your G-d with all your heart, and all your soul, and all your might. These words that I command you today shall be upon your heart. Repeat them to your children, and talk about them when you sit in your home, and when you wlak in the street; when you lie down, and when you rise up. Hold fast to them as a sign upon your hand, and let them be as reminders before your eyes. Write them on the doorposts of your home and at your gates.

This is almost exactly from Deuteronomy VI, 4-9, except for the second line, "Blessed...ever". This line has a more mystical origin. It is said that when Moses ascended Mount Sinai to receive the Ten Sayings, he heard the angels around the divine "throne" saying this line repeatedly. We say it quietly so that the Angels don't know that we have stolen their most important prayer to G-d, however, on Yom Kippur we recite it out loud, so desperate is our need for salvation.
There are a few interesting things to note about the first paragraph: 1) The reference to Israel means Am Yisrael, the People of Israel.
2) "..when you lie down and when you rise up.." refers to the daily praying times,although the Shema is of such importance that when it comes time to say it, no matter what you are doing you must stop and say the Shema - even if you are in a bath you must step out, cover yourself, and say the Holy words.
3) "...a sign upon your hand and as reminders before your eyes..." refers to the laying of tefillin,
4) "..on the doorposts of you home.." means the Mezuzah, a box containing a parchment with the full three verses of the Shema written on.

The second paragraph of the Shema is from Deuteronomy XI, 13-21, and the third is from Numbers XV, 37-41.

The Shema is also recited on death. When Rabbi Akiba was taken out to be killed by the Romans, it was time to read the Shema. As the Romans tore off his flesh with metal combs, he recited the Shema. His disciples cried "Even now?", to which he replied "All my days I was troubled by the explanation "with all your soul" - even if He takes it from you. Now this is in my power, should I not fulfill it?" Rabbi Akiba died as he recited the word One. Thus, Jews try to recite the Shema on their death.