Praying for the Messiah to come is a daily part of prayer in Judaism.
From the Amidah: The heart of the Jewish prayer life consist of a prayer knows as the Amidah (18 Blessings). Often said three times a day, while praying with others, this prayer becomes the cornerstone of each prayer service. The following prayer is included in the daily Amidah.
The offspring of your servant David may you speedily cause to flourish, and enhance his pride through Your salvation, for we hope for Your salvation all day long. Blessed are you, Hashem, Who causes the pride of salvation to flourish.(1)
From the Yigdal: As a part of the daily morning prayers said in many congregations, the Yigdal prayer is often sung or chanted. This prayer focuses on the 13 Articles Of Faith that The Rambam (Maimonides) says every Jew should believe in. The 12th principle is stated as "I believe with complete faith in the coming of Moshiach (Messiah). And though he may tarry, I shall wait anticipating his arrival each day."
There is a prayer recited each week on the sabbath that includes the words: He is our God, He is our Father, He is our King, He is our Saviour. This prayer (Sabbath Amidah, Kedushah) helps to support the position that one person (God) can be all four of these titles at the same time.(2)
Please check out our Master Messiah Page for more on how our Messiah can share all these titles.
The Isaiah 9:6-7 prophecy also teaches about Messiah's different tittles.
This is a blessing recited daily in the Amidah prayer.
This refers to Mashiach ben Yossef.(2) In some Jewish circles two different Messiah's are expected. For more on this please read Two Messiah's.
"We are taught that the ultimate salvation of the Jewish people is possible only through the Davidic Messiah."(3)
Sometimes over 50 prayers a day are said in reference to the coming of the Messiah.(4)
On Passover the Seder meal ends with "Next Year in Jerusalem." This is in direct reference to the Messiah coming and setting up His Millennial Kingdom there.
Read about another Prayer.
1). The Complete Artscroll Siddur p.108
2). The Complete Artscroll Siddur p.464
3). Mashiach: The Principle of Mashiach and the Messianic Era in Jewish Law and Tradition by Jacob Immanuel Schochet (new expanded edition) p.93
4). Lubavitch Chabad of Peoria Jewish Art Calendar 5764 (Nov 2003).