Function over a list that depends on the index

MapIndexed:

MapIndexed[#2[[1]] + # &, {a, b, c, d}]

{1 + a, 2 + b, 3 + c, 4 + d}

Also

Range[Length @ #] + # & @ {a,b,c,d}

{1 + a, 2 + b, 3 + c, 4 + d}

A couple more options --

lst = {a, b, c, d};

Table[lst[[n]] + n, {n, Length[lst]}]

{1 + a, 2 + b, 3 + c, 4 + d}

lst + Range[Length[lst]]

{1 + a, 2 + b, 3 + c, 4 + d}