Are there any mandatory prayers in Christianity?

The Lord's Prayer is the best daily prayer we have. It is meant as a daily prayer simply because of the line "Give us this day our daily bread." And since we sin everyday, knowingly or unknowingly, it adds "And forgive us our sins as we forgive those who sinned against us." This line, in fact, constitutes sanctification - the continual process of being made holy by the power of the Holy Spirit, a lifelong process that makes us more and more like Jesus Christ.

Indeed, it can be argued that the Lord's Prayer itself is the proclamation of our faith in the fulfillment of the will of the Father in His Son, Jesus Christ. It is our Christian Creed, taught by no sinful mortal, but by Jesus Christ himself.

An excellent source is the book "The Creed of Christ: An Interpretation of The Lord's Prayer" by Gerald Heard (1889 - 1971). A well-known author, philosopher and lecturer, Heard studied history and theology at the University of Cambridge, graduating with honours in history. He lectured from 1926 to 1929 for Oxford University's extramural studies programme. More information about him can be sourced from Wikipedia.

In the book, Heard describes The Lord's Prayer as the "real creed of Christianity." On page 6 of his book, he writes:

At the heart of the Gospels there is, however, one other thing. Beside the new Commandments, beside the new Law, more lovely but far more exacting than the old, there is, put more briefly and tersely, a master-instruction, a set of key-rules as to how that Law may be kept. There is only one passage in the biographies more central than the Sermon on the Mount. It is more central because it is the root from which the action ordered by the Sermon must spring, because it shows the source of power without which the Sermon, the Beatitudes, remain a magnificent but impossible demand, a splendid promise which cannot be fulfilled. That passage is therefore rightly called by a supreme title, the Lord's Prayer.

Heard goes on to link faith and the Lord's Prayer (for example, as implied by the following passage, page 94):

It is so against the grain of our present nature to realize that any right prayer must first and foremost be something which alters the self, a process whereby desire is transcended and the will transmuted."Bread of the Coming Day...My bread is to do the Will of Him Who sent me." How are we to do that will which is so different from ours? Are we not here involved in a vicious cycle? To live as God would have us live His eternal Life we have to do His will, but to do His will we have to become part of his Life. As long as we are self-willed, motivated by our wills, we do our wills, not His.

I strongly recommend the book that masterfully examines the Lord's Prayer and raises it to the level where it should be - our Creed.

Truly, there is no place in the Bible where you can find MANDATORY prayer. But Jesus gave us some guidelines on how we should pray and what the content of our prayer should be.

Recommended is the Lord's prayer which I found sufficient to cater for all needs of a christian. This doesn't mean you have to pray it verbatim but reflect on every part of it and pray it in your own words.

The Lord's prayer encourages approaching God in prayer like a child to Father, that every christian should anticipate the coming of christ and value doing the will of God. Daily provision of food, Deliverance from evil, grace not to fall into temptation, forgiveness of sins and so on.

Sticking to this alone is enough for a christian to be sustained in life journey and the christian journey.

To Catholics, observance of the Sabbath as mandated by the 3rd commandment:

Remember the sabbath day—keep it holy. Six days you may labor and do all your work, but the seventh day is a sabbath of the LORD your God.f You shall not do any work, either you, your son or your daughter, your male or female slave, your work animal, or the resident alien within your gates. For in six days the LORD made the heavens and the earth, the sea and all that is in them; but on the seventh day he rested. That is why the LORD has blessed the sabbath day and made it holy. Exodus 20:8-11 NABRE

is observed by the precept of the church

The precept of the Church specifies the law of the Lord more precisely: "On Sundays and other holy days of obligation the faithful are bound to participate in the Mass." "The precept of participating in the Mass is satisfied by assistance at a Mass which is celebrated anywhere in a Catholic rite either on the holy day or on the evening of the preceding day." CCC 2180

and, as a prayer

"The Mass is the most perfect form of prayer" -Pope Paul VI ^{(legit citation appreciated)}

it ranks right up there. Even if one doesn't consider the Mass a prayer, it certainly contains lots and lots of prayers and lots and lots of scripture.

But, there is another prayer that all Christians must pray, because prayer is more than verbal. One must contemplate Jesus

that at the name of Jesus every knee should bend, of those in heaven and on earth and under the earth, and every tongue confess that Jesus Christ is Lord, to the glory of God the Father. Phil 2:10-11 NABRE

And, in so doing, one must pray.

Finally there's the Lord's Prayer, which has been noted elsewhere, I wasn't going to mention it, but people are claiming that it was never meant to be repeated. Well...

To many protestants this:

Neither pray as the hypocrites; but as the Lord commanded in His Gospel, thus pray: Our Father who art in heaven, hallowed be Your name. Your kingdom come. Your will be done, as in heaven, so on earth. Give us today our daily (needful) bread, and forgive us our debt as we also forgive our debtors. And bring us not into temptation, but deliver us from the evil one (or, evil); for Yours is the power and the glory for ever.

Thrice in the day thus pray.

May seem more familiar, or at least the end, and they sure as heck didn't get it from the Bible. I think they got it from the Didache Chapter 8, the apocryphal, but still pretty holy, book of the compiled wisdom of the Apostles, by way of the Catholic Church which preserved the tradition, but lost the manuscript.

So, owing to the age of this book (certainly older than Eusebius of Caesarea who wrote about it in the 4th century), it's pretty clear that the Lord's Prayer was interpreted as "the what to pray" if you want to be a Christian.