According to a book I'm reading (Judaism: Everything You Need to Know About: Jewish Religion) and various other Jews I have talked to say, you can violate the 10 commandments to save a life.
Is this true?
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A general rule is stated in the Talmud (Ketubot 19a):
דאמר מר אין לך דבר שעומד בפני פיקוח נפש אלא עבודת כוכבים וגלוי עריות ושפיכות דמים בלבד
for a Master said: 'There is nothing that comes before the saving of life except idolatry, incest and bloodshed only. (Soncino translation)
(“Incest” is actually an imprecise translation. The term giluy arayot includes a range of forbidden sexual unions.)
As some of the Ten Commandments deal with idolatry, incest (or other sexual unions in the same category, e.g. adultery) and bloodshed, they can not be violated even to save a life. The others can.
There may be certain circumstances in which the others may not be violated as well, but that would be due to external factors (e.g. desecration of God's name), not due to their status as part of the Ten Commandments (and the reason for the exceptions mentioned above is also not due to their status as part of the Ten Commandments).
I. Among the 10 commandments there are 3 that are not overridden by pikuach nefesh (i.e. יהרג ואל יעבור):
II. Additionally, all other commandments cannot be overridden under specific conditions:
If a gentile forces him to violate any one mitzva, not for his own personal benefit, but solely to have him violate the mitzvot, and it is in the presence of ten Jews (בפרהסיא), he should sacrifice his life and not transgress.
or in a time of persecution against obedience to mitzvot (בשעת גזרת מלכות).
(Caveat - I'm not religiously a Jew, I only have a Jewish family background.)
With due respect @Alex and @Kouty - their answers and the sources they quote implicitly regard the saving of the life of a Jew. Non-Jew ("goy") life is held in much lower regard.
As an example, just recently in 2012, the most highly-esteemed religious leader and halachic rule-maker among Sepharadi Jews in Israel, Rabbi Ovadia Yosef, ruled that a doctor should not violate even the commandment of observing the Sabbath to save the life of a Non-Jew. But this is an example of a "in principle X but in practice opposite-of-X": Yosef ruled that because the law requires otherwise (and there are all sorts of reasons to respect non-Jewish state law), it is ok to violate the Shabbat; and that doctors can use a Halachic "trick" to get around the restriction by working in teams of two; etc.
This continues a long line of ambiguous rulings of the same character, which forbid, yet effectively-allow violating the Shabbat to save a Goy (excerpt taken from here):
יסוד ההיתר כדי למנוע סכנה מיהודי מבואר בחת"ס יו"ד קלא, ודברי חיים או"ח ב, כה. וכ"כ אג"מ או"ח ד, עט; רשז"א בשש"כ מ, הערה מז; צי"א ח"ח טו, ו; ח"ט יז, א; יבי"א ח, לח. ויש להוסיף שלרמב"ן (הוספות לעשה טו), מחללים שבת על הצלת גר תושב. וכן דעת רשב"ץ. ויש אומרים שגם בלא קבלת המצוות בפני שלושה מי ששומר בפועל שבע מצוות נחשב כגר תושב (מהרי"ץ חיות, רמ"ד פלאצקי). וכ"כ הרב רבינוביץ' במלומדי מלחמה מג. ולדעת רבים אין מחללים שבת על גר תושב, וגם אין כיום דין גר תושב. אבל לכל הדעות מצילים כמבואר למעלה. ובבית חולים שמתנהל על פי ההלכה, יש להעדיף לקבוע בשבת תורנות לרופאים ואחיות גויים, ואם יגיעו חולים גויים, יטפלו הגויים בגויים. ואם הגיע גוי עם מחלה שהרופא היהודי מומחה יותר ברפואתה, ורגילים בימות החול לפנות אליו במקרים שכאלה, יטפל הרופא היהודי בחולה הגוי, גם במלאכות דאורייתא.
So you have Rabbi Moshe son of Nachman, Rabbi Moshe Sofer (the Hetem Sofer), Rabbi Shimon son of Tzemah Duraan etc. - and these are Halachic heavy-weights going back many many centuries.
Now, the examples I gave so far are just about the Sabbath, which is a relatively "weak" commandment, i.e. there are quite a few excuses for violating it. And on the other end of the spectrum, the super-strong commandments are not violable, as the other answers suggest.
What I really can't tell you is what the deal is with the in-between commandments. For example, is it allowed (in practice) to steal in order to save a Goy's life? I'm sure some Halachic scholars have considered these questions, but better-versed people than me would need to fill you in on that one.
PS - The lives of non-Jews are sometimes forfeit, or you are even commanded to just kill them. For example, non-Jews living in the lands which the Jewish god has promised to Jews/Hebrews - the fundamental principle is that they need to be exterminated, including men women children and livestock see Deuteronomy chapter 20, verses 16-18. But this is not done in practice, and two millennia of post-biblical Halachic scholarship basically say otherwise. I've only provided this quote to emphasize how these things are complex and have contradicting layers of what is required in principle.