Why did Avraham fall upon his face"?
Rashi and Targum Yonasan: Because he was not circumcised 1 (and, Rashi adds, was therefore overcome by fear of the Shechinah and lacked strength to stand). 2
Ramban: To prepare to receive a prophecy (both here, and again in 17:17, where he prepared for the next prophecy). 3
Seforno: To accept the covenant that HaSh-m had made with him, and to thank Him for it.
We find this also by Bil'am, when HaSh-m appeared to him (See Bamidbar 24:4).
Chochmah u'Musar (Vol. 2, p. 338): Even though Avraham was waiting for HaSh-m to command him, lack of the Mitzvah harmed him, just like natural dangers harm even b'Ones. All the more so, how much sin blunts a person!
We find this also in Parshas Korach (Bamidbar 16:22; Bamidbar 17:10).