Snakify a String

Ruby, 87 bytes

->s,n{p=0
a=(' '*(w=s.size)+$/)*n
w.times{|i|a[p]=s[i];p+=[w+1,1,-w-1,1][i/(n-1)%4]}
a}

Some minor abuse of the rule Trailing spaces on each line are allowed. Each line of output is w characters long, plus a newline, where w is the length of the original string, i.e. long enough to hold the whole input. Hence there is quite a lot of unnecessary whitespace to the right for large n.

Ungolfed in test program

f=->s,n{
  p=0                            #pointer to where the next character must be plotted to
  a=(' '*(w=s.size)+$/)*n        #w=length of input. make a string of n lines of w spaces, newline terminated
  w.times{|i|                    #for each character in the input (index i)
    a[p]=s[i]                    #copy the character to the position of the pointer
    p+=[w+1,1,-w-1,1][i/(n-1)%4] #move down,right,up,right and repeat. change direction every n-1 characters
  }
a}                               #return a

puts $/,f['a',3]

puts $/,f['Hello,World!',3]

puts $/,f['ProgrammingPuzzlesAndCodeGolf',4]

puts $/,f['IHopeYourProgramWorksForInputStringsWhichAre100CharactersLongBecauseThisTestCaseWillFailIfItDoesNot.',5]

puts $/,f['!"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~',10]

Pyth, 48 45 44 43 42 bytes

=Y0juXGZX@G~+Z-!J%/HtQ4q2J~+Y%J2@zHlzm*;lz

Try it online.

This approach does the same trailing whitespace abuse as the Ruby answer.

JavaScript (ES6), 143 bytes

(s,n)=>[...s].map((c,i)=>(a[x][y]=c,i/=n)&1?y++:i&2?x--:x++,a=[...Array(n--)].map(_=>[]),x=y=0)&&a.map(b=>[...b].map(c=>c||' ').join``).join`\n`

Where \n represents a literal newline. Ungolfed:

function snakify(string, width) {
    var i;
    var result = new Array(width);
    for (i = 0; i < width; i++) result[i] = [];
    var x = 0;
    var y = 0;
    for (i = 0; i < string.length; i++) {
       result[x][y] = string[i];
       switch (i / (width - 1) & 3) {
       case 0: x++; break;
       case 1: y++; break;
       case 2: x--; break;
       case 3: y++; break;
    }
    for (i = 0; i < width; i++) {
        for (j = 0; j < r[i].length; j++) {
            if (!r[i][j]) r[i][j] = " ";
        }
        r[i] = r[i].join("");
    }
    return r.join("\n");
}