Remove surrounding zeroes of a 2d array

Wolfram Language (Mathematica), 42 bytes

#&@@CellularAutomaton[{,{},0{,}},{#,0},0]&

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Cellular automata are indeed the answer to life, the universe, and everything.¹

How?

CellularAutomaton accepts an input array and an optional background value. Thus, {#,0} specifies that a cellular automaton rule should be applied to the input, assuming a background of 0s.

A neat thing here is that CellularAutomaton crops the output so that no border of background cells is present (because otherwise the output lies on an infinite plane).

The code applies the rule {Null, {}, {0, 0}} -- applying the head Null to the 0-radius neighbor of each cell (i.e. only the center: the cell itself) -- exactly 0 times. The result of this is the original input, but with background removed (i.e. cropping out surrounding 0s).

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^{1. See the bytecount of my answer? ;)}

JavaScript (ES6), 98 bytes

(a,z)=>(g=A=>A.slice(A.map(m=M=(r,i)=>M=(z?a:r).some(n=>z?n[i]:n)?1/m?i:m=i:M)|m,M+1))(a).map(z=g)

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How?

To overcome the lack of a zip built-in, we define a function g() that is able to operate on either the rows or the columns of the input matrix a[ ], depending on the value of the global flag z.

g() looks for the minimum index m and maximum index M of either non-empty rows (if z is undefined) or non-empty columns (if z is defined) and returns the corresponding slice of either the matrix itself or a given row of the matrix.

To summarize:

• we first remove rows by invoking g() on the matrix with z undefined
• we then remove columns by invoking g() on each row with z defined, which leads to this rather unusual .map(z=g)

Commented

(a, z) => (               // a[] = input matrix; z is initially undefined
  g = A =>                // g() = function taking A = matrix or row
    A.slice(              //   eventually return A.slice(m, M + 1)
      A.map(m = M =       //     initialize m and M to non-numeric values
        (r, i) =>         //     for each row or cell r at position i in A:
        M = (z ? a : r)   //       iterate on either the matrix or the row
        .some(n =>        //       and test whether there's at least one
          z ? n[i] : n    //       non-zero cell in the corresponding column or row
        ) ?               //       if so:
          1 / m ? i       //         update the maximum index M (last matching index)
                : m = i   //         and minimum index m (first matching index)
        :                 //       otherwise:
          M               //         let M (and m) unchanged
      ) | m,              //     end of map(); use m as the first parameter of slice()
      M + 1               //     use M+1 as the second parameter of slice()
    )                     //   end of slice()
  )(a)                    // invoke g() on the matrix with z undefined
  .map(z = g)             // invoke g() on each row of the matrix with z defined

MATL, 3 bytes

JYa

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Explanation

J      % Push 1j
Ya     % With complex 2nd input, this unpads the matrix in the
       % 1st input (implicit). The unpad value is 0 by default
       % Display (implicit)