It is sometimes permissible to recite an abbreviated form of the shemoneh esrei in the event that one is simply unable to recite the entire shemoneh esrei. As the Mishna says:
Rabban Gamliel says: Every day a man should say the Shemoneh Esrei. Rabbi Yehoshua says: An abridged Shemoneh Esrei. Rabbi Akiva says: If he knows it fluently he should say the shemoneh esrei, if not, an abridged Shemoneh Esrei.
This “abridged Shemoneh Esrei” is called "havinenu," named after its opening word. It reads as follows:
Grant us wisdom, Hashem, to know Your ways, and circumcise our heart to fear You, and forgive us so that we may be redeemed, and keep us far from our sufferings, and satisfy us in Your land, and gather our dispersed from the four corners of the earth, and judge those who pervert your law, and lift Your hand against the wicked, and let the righteous rejoice in the building of Your city and the establishment of Your temple, and the rise of David Your servant, and the preparation of a light for the son of Yishai the Mashiach, even before we call out to You may You answer us, Baruch Atah Hashem shomeiah tefilla.
Havinenu may only be recited in the most extenuating circumstances. According to the Shulchan Aruch, “extenuating circumstances” is defined as one who is travelling and fears that he will be unable to recite the standard shemoneh esrei without being interrupted, or will otherwise be unable to properly concentrate. There are a number of other emergency situations when reciting havinenu would be justified, as well. Nevertheless, it is questionable whether one who recited havinenu, when not truly called for, has discharged his requirement to pray.
Havinenu is not a stand-alone prayer. When reciting Havinenu, one first recites the three opening blessings of the shemoneh esrei, then havinenu is recited, and then one concludes the prayer with the last three blessings of the shemoneh esrei. Hence, havinenu is essentially a substitute for the thirteen middle blessings of the shemoneh esrei. Indeed, one will note that the wording of havinenu is actually an abbreviated form of these thirteen middle blessings. The havinenu formula may not be used when seasonal or festive additions must be added into the shemoneh esrei. For example, since Havinenu makes no allowance to insert “atah chonantanu,” as is required on motzai Shabbat, it may never be recited at that time. At all such times, one has no choice but to recite the full shemoneh esrei.
Nevertheless, virtually all contemporary halachic authorities are of the opinion that havinenu should not be recited at all nowadays. This is because most, if not all, of the possible justifications for reciting havinenu in place of the shemoneh esrei are no longer applicable. So too, one who is unable to recite the full shemoneh esrei with even a minimal level of concentration will likely not be able to recite havinenu with minimal concentration, either. As it says:
In our times we have never heard of someone who would recite Havinenu and the reason is clear. In previous generations they would pray with much concentration; they established Havinenu for those who were unable to properly concentrate. However, in our day when we do not properly concentrate…what would be the purpose of Havinenu?
Indeed, most siddurim do not even include the havinenu text anymore. It is interesting to note that the Talmudic sage Abaye was vehemently opposed to using havinenu in place of shemoneh esrei, and would even curse one who did so.
 Berachot 29a; OC 110:1.
 There is a slightly different version of this prayer found in Chayei Adam 24:19. See also Kaf Hachaim, OC 110:5.
 OC 110:1.
 Mishna Berura 110:1.
 Aruch Hashulchan, OC 110:6. See also Biur Halacha 110.
 Berachot 29a; Aruch Hashulchan, OC 110:6; Shulchan Hatahor; Zer Zahav 110:1.