There is an interesting Halacha related to the recitation of קריאת שמע. There is a difference of opinion between בית שמאי and בית הלל as to how to recite the Shema.
Beit Shammai felt that we take the Torah literally. We must read the Shema lying down at night and in a standing position in the morning. Beit Hillel held the key words were ובלכתך בדרך, in the manner we are walking.
The Halacha is like Beit Hillel and we can say the Shema while we are walking. Nevertheless, even when we are walking, we must stop and stand still for the first line of Shema. Tosfot tells us that this is the most important verse in Shema where we are to accept upon us the yoke of Heaven. One cannot focus and concentrate while walking in the same way that he concentrates while standing still.
So we must remember to say Shema standing. However, if we were in a sitting position, we are allowed to remain sitting.