The Mishna (Pesachim 116a) records the observance of the mitzvah of "sippur yetzias mitzrayim" on the first night of Pesach. " Arami oveid avi" (normally recited in connection with the bringing of bikkurim) is recited, and the comments of the Torah Shabaal Peh are interspersed between the various phrases of the several pesukim.
Commenting on the posuk, "Vanitzak el Hashem Elokei Avoseinu", ("and we cried out in prayer to our G-d and He listened to our prayers, etc." Devorim 26:7) we quote the posuk from this week's parsha (Shemos), "And it came to pass that the King of Egypt died, and the Jewish people cried out from their labor, and their cries went up to G-d from their labor." This posuk from parshat Shemos is cited in order to better understand the meaning of the posuk in Mikra Bikkurim. When we say that, "we called out to G-d in prayer and that He answered our prayers", the Torah Shebaal Peh comments that this is not to be taken literally! The Jewish people never really prayed! G-d in His infinite kindness considered their crying out from their hard labor under the Egyptians as if they had prayed, and this unspoken prayer was answered.
But why should G-d consider the crying out from pain and agony as if the Jewish people had offered a prayer? It would appear that prayer is so essential and intrinsic to the human soul that we assume that subconsciously man would always like to pray. The Rabbis of the Talmud formulated as a halacha (Brachos 21a) that we would wish that man would be able to pray all day long.
During the first five days of creation the Torah tells us (Bereishis 2-5) that nothing was yet growing because it had not yet rained because man had not yet been brought upon the scene "to work the earth". The Rabbis (see Rashi there) understood that expression ("to work" - "laavod") to mean that man was not yet around to pray ("avoda shebalev") for the rain, and G-d was not going to have it rain until man asked for it! One of the most important roles of man is to pray.
In the opening mishna in Bava Kamma, the tanaiim list off the four basic categories of damages. One of them is entitled "maveh", and the Rabbis had two differing traditions regarding the meaning of the term (see Meiri). According to one tradition, the expression, "maveh", means "the one who prays", and is a reference to the human being who apparently is created in order to pray.
Although G-d is infinite and shoulders the burden of taking care of the entire creation, He created man "in His image" to enable man to communicate with Him. This is one of the Thirteen Principles of our faith: We believe in prophecy. Included in this principle of prophecy is that we also believe in prayer. We believe that there can be communication between G-d and man: G-d has communicated with man by means of prophecy, and man has been given the privilege of communicating with G-d by means of prayer.
Man's ability to pray is considered so fundamental and obvious that (according to Ramban) it does not need to be included in the listing of the 613 mitzvos. Ramban feels that the obligation to daven daily is only rabbinic and therefore ought not to be included in the listing of the 613 biblical mitzvos; and the obligation to pray "in times of great distress", although biblical in nature, ought also not be counted among the listing of the mitzvos. If one has emunah in the principles of our faith, it will be self evident that we will chose to daven. (See Iggros Moshe O.C. II #24).
I remember the scene, over forty years ago, on a Purim, in the middle of the chagiga, when one of the students sang a famous Yiddish folk song. When he got to the line that says that "he must daven because he is a Jew" ("davenen muz er"), Rabbi Lifshitz, zt"l, called out, in correction of the lines of the poem, that "he wants" to daven (" davenen vill er")!