Well, looking at the "List of awards won by the Land Before Time" on the wikia, here is what we got, for the whole series:
It's got 3 Young Artist Awards nominations and 2 wins
2 Saturn Awards nominations
6 Annie Awards, with 1 win.
12 DVD Exclusive Awards nominations for the sequel series. 4 for Best Movie Premiere, 4 for Best Character Perfomance and 4 for Best Original Song.
1 Motion Picture Sound Editors award nomination.
So, nothing major (though Annie awards are pretty prestigious, I think), and certainly nothing from the Academy. Kinda funny how none of the 3 awards they DID win were for the original.