Broadly speaking, the Old Testament is considered sacred by all three. However, it must be noted that between the three religions (and even within Christianity itself) what the Old Testament comprises and how it is to be read are quite different.
Judaism: Jews use the Tanakh, or the Masoretic Old Testament text, and see it as the basis of their Religious Law which has developed in the same way for nearly 2500 years. To read more about this, see the Related Question below.
Christianity: Christians use the Old Testament based on the Septuagint Translations of the Masoretic Text which added several chapters onto certain books, changed a few key words, and added additional books as well, called the Deuterocanon. Different Christian sects may increase or decrease the amount of these Deuterocanonical books. The Old Testament primarily serves to give the background and purpose for the Arrival of the Christ and the Foundation of the New Covenant.
Edit: The above statement regarding Christianity and the Old Testament is wrong. The Septuaginta ("LXX") i not a translation of the Masoretic text. The Septuagint is a Greek translation of the Tanakh or written Torah as this existed in or around the year 200 before the birth of Christ. This was long before the socalled Masoretic text even existed. The Greek translation was made by Jews, partly as a commission, and partly because there were many Jews in Egypt, especially in the metropolis Alexandria, who spoke Greek, not Hebrew. The Masoretic text came after the Septuagint, and the Septuagint is likely more in accordance with the ancient Hebrew scriptures than the Masoretic version.
Islam: Muslims read the Old Testament as a guide to understanding the moral lessons given in the Qur'an. The morality of the Old Testament is secondary to that of the Qur'an and any discrepancy between the Old Testament and Qur'an is judged to be an error in the earthly Old Testament. To read more about this, see the Related Question below.
Judaism, Christianity, Islam
Islam, Christianity and Judaism
Judaism, Christianity, and Islam religions.
The three major monotheistic religions are Judaism, Christianity, and Islam. These religions believe in one God and have sacred texts such as the Torah, the Bible, and the Quran.
The three are Christianity, Islam and Judaism. Three other sacred religions are Hinduism, Buddhism and Shintoism.
-- Islam -- Judaism -- Christianity
Islam, Judaism and Christianity.
Judaism, Christianity, and Islam have all claimed the Holy Land for themselves.
Christianity and Judaism
Three religions with holy sites in the eastern Mediterranean are Christianity (including sites like Jerusalem and Bethlehem), Judaism (with sites such as the Western Wall in Jerusalem), and Islam (with sites like the Dome of the Rock and Al-Aqsa Mosque in Jerusalem).
Islam, Christianity & Judaism
Christianity and Islam ^^