Node, 145 142 bytes

for(s=process.argv[2],d=new Date;s[a=(new Date-d)/1e3|0]+console.log(s.replace(/./g,(c,i)=>i<a?c:String.fromCharCode(32+Math.random()*95))););

This seems a little long, and there's probably a little room for golfing. Note that the semicolon at the end is required; without it the program throws a syntax error because the for statement has no body.

Outputs way more than 20 lines per second; a little birdie told me that it's roughly 12 thousand. Here's how it looks in the ConEmu terminal emulator on my computer (recorded at 30 fps):

HTML/JavaScript, 170 bytes

setInterval(_=>o.textContent=i.value.replace(/./g,(c,i)=>Date.now()-d>++i*1e3?c:String.fromCharCode(Math.random()*95+32)),d=50)

<input id=i oninput=d=Date.now()><pre id=o>

BASH, 99 93 92 91 88 bytes

with tr + head + urandom

while ((${#1}-n));do
echo "${1::n=SECONDS}`tr -dc \ -~</dev/ur*|head -c$[${#1}-n]`"
done

(thx. to @manatwork )

Bash, 247 245 212 207 bytes

R()(echo $SECONDS);w=`R`;until [ "$a" = "$1" ];do for i in `seq 1 $[${#1}-${#a}]`;{ a+=`printf "\x$(printf %x $[$RANDOM%127+32])"`;};echo -e "$a\r";a=${1:0:q};((`R`-w>0))&&{ w=`R`;((q++));}||:;done;echo "$a"

Thanks a lot Bash for being so whitespace sensitive...

Anyways, output is given in real time on separate lines. Save as a .sh script and invoke with:

bash <File Name>.sh <Input>

For example, bash Cracking_In_Progress.sh okayerty results in the following output, recorded at 30 frames per second:

Pyth - 27 24 bytes

This actually looks pretty cool :D

WJ-lQKs.d1+<QKsmOr;\~J;Q

Try it online here (obviously not in real time, but if you scroll it down with a steady hand).

WinDbg, 400 391 bytes

.for(r$t1=@$t0;by(@$t1);r$t1=@$t1+1){};m@$t0 L@$t1-@$t0+1 @$t1+1;r$t4=2*@$t1+2-@$t0;r$t8=@$t4+f;r$t3=0;.for(r$t2=0;@$t2<@$t1-@$t0;da@$t0){.for(r$t7=@$t0+@$t2;by(@$t7);r$t7=@$t7+1;r$t8=@$t8+1){eb@$t7 by(@$t8)%5e+20};r$t9=0;.foreach(p {.echotime}){.if7==@$t9{ea@$t4"p";.if1>@$t3{r$t3=by(@$t4+7)}};r$t9=@$t9+1};j@$t3!=by(@$t4+7)'m@$t0+@$t4-@$t1+@$t2-1 L1 @$t0+@$t2;r$t2=@$t2+1;r$t3=by(@$t4+7)'}

-9 bytes by simplifying some math

This definitely does not seem to be the kind of thing WinDbg is intended to do. ;)

Input is taken by entering an ascii string at a memory location and setting that address to the pseudo-register $t0. Eg:

r$t0 = 2000000
eza @$t0 "abcde"

The prng I'm using is whatever the contents in memory, some bytes past the input string. Chrome.exe appears to fill the memory space after 0x2000000 with random-looking-enough bytes so I used a dump of chrome.exe. Unknown if this is uniform, but looks random-enough to me.

How it works:

.for(r$t1=@$t0; by(@$t1); r$t1=@$t1+1){};         * From $t0, increment $t1 until the byte
                                                  * at $t1 is 0 to find length of input
m@$t0 L@$t1-@$t0+1 @$t1+1;                        * Duplicate input (memory 
                                                  * becomes: "input\0input\0")

r$t4=2*@$t1+2-@$t0;                               * Set $4 to the byte after \0 of the 
                                                  * duplicated input
r$t8=@$t4+f;                                      * Set $t8 to $t4+15, this is the prng
r$t3=0;                                           * Init $t3=0, this will hold the time

.for(r$t2=0; @$t2<@$t1-@$t0; da@$t0){             * For $t2=0, loop until it's input length,
                                                  * printing the string at $t0 after each
                                                  * loop. $t0 is where the password crack
                                                  * progress is written.
    .for(r$t7=@$t0+@$t2; by(@$t7); r$t7=@$t7+1;   * Loop over each uncracked char
                                   r$t8=@$t8+1){  * also incrementing prng ($t8)
        eb@$t7 by(@$t8)%5e+20                     * Write a visible ascii char onto the
                                                  * uncracked char position based on the 
                                                  * current byte of prng%0x5e+0x20 (prng%126+32)
    };

    r$t9=0;                                       * Set $t9=0 for updating current time
    .foreach(p {.echotime}){                      * For each (string) word in a statement
                                                  * like "Debugger (not debuggee) time: Mon 
                                                  * Nov 21 18:23:08.433 2016 (UTC - 8:00)"
        .if7==@$t9{                               * If the 7th word, ie- the current time
            ea@$t4"p";                            * Write the time at $t4
            .if1>@$t3{                            * If $t3 has not been set yet
                r$t3=by(@$t4+7)                   * ...save the current second in $t3
            }
        };
        r$t9=@$t9+1                               * Increment $t9 until it's 7
    };

    j@$t3!=by(@$t4+7)'                            * If the current second has changed
        m@$t0+@$t4-@$t1+@$t2-1 L1 @$t0+@$t2;      * Copy the cracked char from dupe input
        r$t2=@$t2+1;                              * Increment $t2 (loop ends when this is input length)
        r$t3=by(@$t4+7)                           * Save the new current second
    '
}                                                 * Final crack is printed by for loop

Note: Some bytes could be golfed by using j instead of the .if's, but that causes it to run too slowly on my machine so it doesn't output at least 20 lines per second, so not saving those bytes.

Sample Output: http://pastebin.com/H4H74sAx

MATL, 26 bytes

`GZ`:)' ~'olGn4Mk-I$YrhD7M

Try it online!

Below is the real-time output from the offline compiler. Note that the animated GIF was recorded at 20 fps to keep its size small, but the actual speed is much greater.

C, 182 176 128 bytes

Golfed:

i;s;n;x=0;g(char*c){s=time(0);while(c[++x]);do{n=time(0)-s;for(i=0;i<x;i++)putchar(i<n?c[i]:32+rand()%95);puts("");}while(n<x);}

Ungolfed:

#include "stdio.h"
#include "stdlib.h"
#include "time.h"
int i,s,n,x=0;
void g(char* c) {
  s = time(0); //Get the initial time
  while(c[++x]); // x = strlen(c) (happy about this one)
  do {
    n = time(0) - s; //seconds since beginning
    for(i = 0; i < x; i++)
      //after each second, print another char of the password
      putchar(i < n ? c[i] : 32 + rand() % 95);
    puts("");
  } while(n < x); //while we haven't printed the whole word
}

I've heard that it's possible to drop some standard #includes, but I couldn't get it to work on the MingW GCC compiler I just downloaded. Also couldn't figure out how to #define b #include without using more space than it was worth. I'm just an idiot, it works fine without them.

05AB1E, 30 bytes

gFžcUNV[¹Y£žQ.r¹gY-£J,XžcÊ#}¹,

Uses the CP-1252 encoding. Try it online!

Please help me golf this down.

R, 138 bytes

z=Sys.time;n=nchar(x<-scan(,""));s=z();t=0;while(t<=n){t=t+z()-s;cat(substr(x,1,f<-floor(t)),intToUtf8(sample(32:126,n-f,T)),"\n",sep="")}

Reads input from stdin.

Counted approximately 61 lines on my machine between each additional letter in the "password".

Python 3, 167 166 bytes

import time,random
t=time.time
p,s=input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)

Reads input from stdin. A 171-byte version runs under Python 2 (replaced input with raw_input):

import time,random
t=time.time
p,s=raw_input(),t()
while t()-s<len(p):print(p[:int(t()-s)]+''.join(chr(random.randint(32,126))for _ in range(len(p)-int(t()-s))))
print(p)

Ungolfed:

import random
import time

p = input()
start = time.time()
while time.time() - start < len(p): 
    print(
        p[:int(time.time() - start)] + 
        ''.join(chr(random.randint(32, 126)) for _ in range(len(p) - int(time.time()-start)))
    )
print(p)

Java 7, 271 265 bytes

void c(String s)throws Exception{String x="",r;for(char c=32;c<'~';x+=c++);for(int i=0,j,l=s.length();i<=l*20;i++){r="";Thread.sleep(45);for(j=0;j<i/20;r+=s.charAt(j++));for(;j++<l;r+=x.charAt((int)(Math.random()*94)));System.out.println(r);if(s.equals(r))return;}}

Ungolfed:

void c(String s) throws Exception{
  String x = "",
         r;
  for(char c = 32; c < '~'; x += c++);
  for(int i = 0, j, l = s.length(); i <= l*20; i++){
    r = "";
    Thread.sleep(45);
    for(j = 0; j < i/20; r += s.charAt(j++));
    for( ; j++ < l; r += x.charAt((int)(Math.random()*94)));
    System.out.println(r);
    if(s.equals(r)){
      return;
    }
  }
}

Input: abcde
Output:

C#, 203 197 195 bytes

Golfed:

void F(string s){int l=s.Length,t=0;var w=new Stopwatch();w.Start();do{if(w.Elapsed.Seconds>t)t++;Console.WriteLine($"{s.Substring(0,t)}{Path.GetRandomFileName().Substring(0,l-t)}");}while(t<l);}

Ungolfed:

    void F(string s)
    {
        int l = s.Length, t = 0;
        var w = new Stopwatch();

        w.Start();

        do
        {
            if (w.Elapsed.Seconds > t)
                t++;

            Console.WriteLine($"{s.Substring(0, t)}{Path.GetRandomFileName().Substring(0, l - t)}");
        } while (t < l);
    }

l stores input length.

StopWatch and Path.GetRandomFileName() are parts of .NET framework.

EDIT1: Implicit type of Stopwatch declaration.

EDIT2: l initialization moved to declaration.

05AB1E, 26 bytes

I post this as a different answer with respect to the other 05AB1E answer since the approach is different

.põ¸ì¨vT·FyžQ.r¹gyg-£«}}¹»

.p                         Generate ordered prefix of input (e.g., ["a", "ab", "abc", "abcd", "abcde"] for "abcde")
  õ¸ì                      Prepend an empty string (e.g., result is ["", "a", "ab", ...])
     ¨                     Strip the last element (the same string as the input)
      v                    For each string in the array
       T·F                 For N in range(20)
          y                Push the current string
           žQ.r            Push all printable characters, shuffled
               ¹gyg-       Take the difference between the length of the input and the length of the current string -> x
                    £      Take the x first characters from the shuffled printable characters
                     «     Yield currentString + shuffledCharacters
                      }    End inner for
                       }   End outer for
                        ¹  Push input (last iteration)
                         » Join everything with newlines and implicitly display

Try it online!

ForceLang, 322 bytes

Noncompeting, requires language features that postdate the question.

def s set
s g goto
s W io.writeln
s k io.readln()
s T timer.new()
def a T.poll()
label 1
s P math.floor a.mult 1e-6
if P=k.len
g 6
s j 0
s t ""
if P=0
g 4
label 3
s v k.charAt j
s t t+v
s j 1+j
if j-P
g 3
label 4
if j=k.len
g 5
s r 94.mult random.rand()
s v string.char 32+r
s t t+v
s j 1+j
g 4
label 5
W t
g 1
label 6
W k

Python3, 149 141 139 bytes

import time,random
i,x=input(),0;l=len(i)
while x<l:x=int(time.clock());print(i[:x]+"".join(chr(random.randint(32,126))for _ in"a"*(l-x)))

Input from stdin.

Eyes version (157 bytes):

import time,random
p,i,x=print,input(),0;l=len(i)
while x<l:x=int(time.clock());p(i[:x]+"".join(chr(random.randint(32,126))for _ in"a"*(l-x)),end="\r")
p(i)

Haskell (GHC), 202 bytes

import System.Random
import Control.Concurrent
f s|l<-length s=mapM_(\n->putStr('\r':take n s)>>mapM(\_->toEnum<$>randomRIO(32,126))[1..l-n]>>=putStr>>threadDelay 50000)$[n|n<-[0..l-1],f<-[1..20]]++[l]

-5 bytes without fancy carriage return action