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Pascal did, but I believe that was because index 0 contained an 8-bit length. There was no need for null termination, and strings were limited to 255 bytes.

Fortran, Matlab, and Julia all start arrays at 1, either always (Matlab) or by default (Fortran, Julia).

Erlang indexes starting at one, except when it doesn't.

Tuples are 1 indexed, lists are 1 indexed (in the standard library, anyway), but binaries are zero indexed.