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We define the following lists:

list = {x, x^2, x^3};
rules = {x -> 1, x -> 2, x -> 3};

And then we can run

Inner[ReplaceAll, list, rules, List]

ReplaceAll @@@ Thread[{list, rules}]

Table[list[[i]] /. rules[[i]], {i, Length@rules}]

fnctn = #1 /. #2 & @@@ Transpose@({##}) &;

fnctn[list, rules]

MapIndexed[#^# &, Range@Length@list]

Last /@ Power[List @@@ rules, Range[Length@rules]]

7. Anyone likes While? I don't but it works

Module[{return = {}, i = 1, end = Length@list},
 While[i <= end,
  AppendTo[return, list[[i]] /. rules[[i]]]; i++]; return]

8. (I hate myself) using For because...why not?

Module[{return = {}}, For[
  i = 1, i <= Length@list, i++,
  AppendTo[return, list[[i]] /. rules[[i]]]];
 return]

9. After a lot of trial and error

smthng = {#1 /. #4, #2 /. #5, #3 /. #6} & @@ (## & @@@ {##}) &;
smthng[list, rules]

All of the above give

{1, 4, 27}