Here is another answer that creates a reusable function to pair up two vectors. The function uses a pure function that maps over the length of the shortest vector to create the pairs.
list1 = {1, 2, 3, 4, 5};
list2 = {13, 18, 20, 18, 13};
pairUp[xValues_ , yValues_] := ({xValues[[#]], yValues[[#]]}) & /@
Range[Min[Length[xValues], Length[yValues]]];
pairUp[list1, list2]
(*
{{1, 13}, {2, 18}, {3, 20}, {4, 18}, {5, 13}}
*)
Hope this helps,
Edmund
PS: New to Mathematica and hoping to improve my understanding by trying to answer a few questions on here from time to time.
Riffle[list1, list2]~Partition~2