Whay does my Backspace key not delete in vi?
Is this a new keyboard? I wonder if it's outputting a slightly non-standard code for backspace, one that many programs accept, but vim does not. Try CTRL-H - that should work as backspace in vim.

You can find out the code your backspace key outputs by going to Terminal, then Preferences>Settings>Keyboard and double-clicking any key in the list. Make sure "Send Text:" appears in the dropdown next to "Action:" Press your backspace key and its code will appear in the box. Make sure to click cancel so you don't change a mapping here. (Mine reports \177 on an Apple keyboard.)

You'll then need to convince Vim to respond to that code. This tutorial looks like it will explain that process. http://vim.wikia.com/wiki/Mapping_keys_in_Vim_-Tutorial(Part_1)

Of course, you could also look for a different keyboard.

References:
http://www.tldp.org/HOWTO/Keyboard-and-Console-HOWTO-5.html
http://vim.wikia.com/wiki/Mapping_keys_in_Vim_-Tutorial(Part_1)
http://hea-www.harvard.edu/~fine/Tech/vi.html