TRAVELING: Airplane or long distance
One who recites the first verse of Shema` without intention, does not fulfill his obligation. (Hilkhoth Kri’ath Shema` 2:1). RMb"M holds he must repeat it with proper intention (Hilkhoth Tafilah 4:15). If he is walking on foot, he must stop for the first verse. A person may recite the rest while standing, walking, lying down or riding an animal….. He may recite the rest of the Shema` while walking. (This is so he can concentrate his intentions—Site Admin). This is a summary of the first few chapters of MT/ Hilkhoth Kri’ath Shema`. The idea of praying on a moving plane should be okay (as long as one can still concentrate—in my estimation). However, halakha 12 (in chp 2 of Hilkhoth Kri'ath Shema`) states that one must be fully awake for the first verse. So I would say that one must decline Shema` until one is fully awake. This doesn’t always go smoothly on a plane.
Regarding one who comes in from a journey, he “may not pray until he composes himself". "Therefore, one who comes in from a journey and is tired or irritated is FORBIDDEN TO PRAY until he composes himself. Our sages taught that one should wait three days until he rested and his mind is settled, and then he may pray.” (Hilkoth Tafilah 4:15/ Eruvin 65a)