The Gemara (Berakhos 4b) states that one should preface the Shemoneh Esreh with the verse "ה' שפתי תפתח... O Lord, open my lips; and my mouth shall declare Your praise" (Psalms 51:17). If you look in most prayerbooks, there is another prefatory verse that precedes this -- "כי שם ה' אקרא... For I will proclaim the name of the Lord; acknowledge the greatness of our God" (Deut. 32:3).* However, this verse only appears prior to the Mincha (afternoon) and Mussaf (holiday additional) services. But it does not appear prior to the Shacharis (morning) and Ma'ariv (night) services. Why is this?
I came up with the following theory many years ago, which I later discovered to be explicit in the commentaries on Shulchan Arukh (Orach Chaim 111:1): The same Gemara that mentions the practice of beginning Shemoneh Esreh with Ps. 51:17 asks how it is permissible to do so. Is there not a concept of being somekh ge'ulah li-tefillah, directly connecting the the Shema's message of redemption with the prayer of Shemoneh Esreh? If so, one should not be allowed to say anything other than words of prayer, so as not to interrupt the continuation. The Gemara answers that since Ps. 51:17 was added to the Shemoneh Esreh, it is considered an extension of the prayer and therefore not an interruption. But it does not say that about Deut. 32:3. Therefore, in Shacharis and Ma'ariv, when we recite Shema (and its blessings) and then proceed directly into Shemoneh Esreh, we cannot interrupt with an extra verse. But in Mincha and Mussaf, when we do not recite Shema and there is therefore no problem of interrupting, one may add this extra verse.
* Just because it appears in the prayerbooks does not mean that it has to be said. I actually do not say this verse. The following is from the Machazor Mesoras Ha-Rav Le-Yom Kippur, p. xxxvi par. 7:
The Rav [R. Joseph B. Soloveitchik]'s custom was not to say the verse כי שם ה' אקרא (Deuteronomy 32:3), prior to the Shemoneah Esrei of Mussaf or Minchah, since the practice to recite it is not found anywhere in the Gemara, as noted by the Vilna Gaon in Beur HaGra to Orach Chaim 111:1, s.v. ולא בשום (R' Menachem Gopin; see also Nefesh HaRav, p. 152).In fact, Dr. Seligmann Baer's Siddur Avodas Yisrael does not have the verse printed in front of Shemoneh Esreh at all.