Minhag S'fardi is to stand up only for the Amidah and Aleinu. However, if you are an Ashkenazi, then the Amidah is not the only prayer that must be said standing.

To begin with, you should don Tefilin whilst standing. In addition, it is customary to recite Birchos ha'Shachar (the morning B'rachos) standing, and one should certainly do so whilst reciting 'Baruch she'Amar', from 'Vayevarech David' until (and including) 'Yishtabach, and 'Aleinu'. And one is also supposed to stand for every Davar she'bi'Kedushah (Kadish, Kedushah and Barchu).

Perhaps the Amidah is more stringent than the others, inasmuch as one is actually standing before Hash-m, and consequently, even in a case of emergency, one should make every effort to stand for the Amidah more than by the other Tefilos. Lechatchilah (initially) however, one should stand for all of the above.

R. Eliezer Chrysler