Q:

Ignore some values at return

Is there Mathematica analogue of Python _ (underscore) or Matlab ~, a special variable, that can be used when a function returns a list and only some of the list elements are needed while others just ignored. E.g.:
f[x_] = {x^ 2, x^ 3};
{a1, _} = f[2]

A:

I would recommend to write
a1 = f[2][[1]]

4

Clear[a1]

{a1, _} = f[2];

also assigns 4 to a1 but produces an error message which you can turn off temporarily with Quiet:
Quiet[{a1, _} = f[2]];

a1

4

A:

Instead of an underscore, a "throwaway" symbol can be used.  For instance,
f[x_] = {x^2, x^3, x^4, x^5};
{a1, z, z, a2} = f[2]

a1 and a2 have their desired values, and the others are overwritten into z at the cost of only a single symbol.

