Many have the practice — conscious or not — to raise their hands, or otherwise gesticulate, whilst in the midst of praying. This is most common during the Amidah, more commonly known as Shemoneh Esrei. While for many this comes out of a deep concentration and a genuine emotional state during tefillah, there may be a number of problems with praying in such a manner.
The Zohar & Pirkei DeRebbe Eliezer
Rabbi Akiva Eger (OC:89) states that one should not pray with outstretched arms so as to be in accordance with the Zohar that makes the point repeatedly that doing so is prohibited. Pirkei DeRebbe Eliezer, an aggadic/midrashic work, apparently makes this point many times as well.
The reason for this prohibition is due to the fact that the nations of the world now pray/behave in such a manner. As such, it would fall under the prohibition of “לא תקים לך מצבה אשר שונא וכו” (Devarim 16:22). While many of the great characters of Tanach did indeed pray in such a manner, now that it has been adopted by the nations of the world, for us to do so would thusly be prohibited.
Piskei Teshuvos
Piskei Teshuvos (95) states that when one raises one’s hands during prayer out of genuine emotion and excitement during prayer, such a thing is a good sign that he is praying from his heart and that his prayers will be accepted. Piskei Teshuvos adds the caveat, however, that if one has in mind to pray in such a manner from the start the Zohar states that “things will not end well for him” (or something along such sinister lines). Indeed, the Zohar continues, praying in such a manner requires an absolutely pure heart, and as such should not be practiced by anyone but the most exceptional amongst us, and only at certain times.
Piskei Teshuvos also quotes Rav Avraham Ben HaRambam as saying that, at least for the opening and closing three brachos of the Amidah, one should be careful not to spread his or her hands apart.
Intentions
While the above sources are far from any sort of consensus on the issue — and are not at all comprehensive enough to declare praying with raised arms prohibited — the issue is not as simple as it would appear at first blush. Indeed, while many see people that daven in such a way as somehow being superior, it may well be the other way around (especially if done with improper intentions).
For further discussion on the subject, and for the location from which I got the above sources, see here.