Because big-endian matches how most humans have done it for most of history ("five hundred twenty one" is written "521" or "DXXI", not "125" or "IXXD"). Because the left-most bit in a byte is the high-order bit, so the left-most byte in a word should be the high-order byte. Because ordering two 8-character ascii strings can be done with a single 8-byte integer compare instruction (with the obvious generalizations). Because looking for 0x12345678 in a hex dump (visually or with an automatic tool) isn't a maddening task. Because manipulating 1-bit-per-pixel image data and frame buffers (shifting left and right, particularly) doesn't lead to despair. Because that's how any right-thinking person's brain works.

The one place I've seen little-endian actually be a help is that it tends to catch "forgot to malloc strlen PLUS ONE for the terminating NUL byte" bugs that go undetected for much longer on big-endian machines. Making such an error means the NUL gets written just past the end of the malloc, which may be the first byte of the next word in the heap, which (on many implementations of malloc) holds the length of the next item in the heap, which is typically a non-huge integer. Thus, on big-endian machines, you're overwriting a zero (high order byte of a non-huge integer) with a zero, so no harm done, and the bug is masked. On little-endian machines, though, you're very likely clobbering malloc's idea of the size of the next item, and eventually it will notice that its internal data structures have been corrupted and complain. I learned this lesson after we'd been shipping crash-free FrameMaker for years on 68000 and Sparc, and then ported to the short-lived Sun386i.