Software to render formulas to ASCII art I guess all computer algebra systems have command line interfaces which render formula as 2D monospace "ascii art". But the only standalone tool to render TeX to 2D I know is tex2mail (comes with PARI/GP).
Are there other standalone programs or libraries for that task, preferably making advantage of various Unicode symbols? Or maybe there is a CAS capable for that.
What I'm talking about:
FriCAS:
            ┌──┐
       x   \│%A
     ┌┐  %e
     │   ─────── d%A
    └┘       2
           %A

tex2mail:
         +-+                              
     ,- \|x   2                              
     | e    /x    dx                              
    -'                 

Maxima:
     /   sqrt(x)
     [ %e
     I --------- dx
     ]     2
     /    x

Those are meant to represent:
$$\int \frac{e^{\sqrt x}}{x^2} \, dx$$
 A: If you are on *NIX platforms you can use asciitex. 
There is also aamath which does a great job in traslating the equation to ascii text files. 
If you don't want to install anything locally take a look at http://ascii.gallery/matheq which I believe is a web wrapper over aamath.  
A: You can use this Web Application:
Diagon


*

*No need to download anything

*Supports ASCII and Unicode.

*Supports other kind of ASCII art diagrams.


Examples:

sum(i^2, i=0, n) = n^3/2+n^2/2+n/6

output (Unicode)

  n                   
 ___        3    2    
 ╲     2   n    n    n
 ╱    i  = ── + ── + ─
 ‾‾‾        2    2   6
i = 0                 

output (ASCII): 

  n                   
 ===        3    2    
 \     2   n    n    n
 /    i  = -- + -- + -
 ===        2    2   6
i = 0                 



mult(i^2, i=1, n) = (mult(i, i=1, n))^2

                    2  
   n        ⎛  n    ⎞   
 ━┳┳━   2   ⎜━┳┳━   ⎟   
  ┃┃   i  = ⎜ ┃┃   i⎟   
 i = 1      ⎝i = 1  ⎠                         



sqrt(1 + sqrt(1 + x/2))

     _____________
    ╱        _____
   ╱        ╱    x
  ╱        ╱ 1 + ─
╲╱   1 + ╲╱      2



[1,2; 3,4] * [x; y] = [1*x+2*y; 3*x+4*y]

⎛1 2⎞   ⎛x⎞   ⎛1 ⋅ x + 2 ⋅ y⎞
⎜   ⎟ ⋅ ⎜ ⎟ = ⎜             ⎟
⎝3 4⎠   ⎝y⎠   ⎝3 ⋅ x + 4 ⋅ y⎠



int(x^2/2 * dx ,0 ,1) = n^3/6

1             
⌠  2         3
⎮ x         n 
⎮ ── ⋅ dx = ──
⌡  2         6
0             



phi = 1 + 1/(1+1/(1+1/(1+1/(1+...))))

                 1         
φ = 1 + ───────────────────
                   1       
        1 + ───────────────
                     1     
            1 + ───────────
                       1   
                1 + ───────
                    1 + ...

Disclaimer: I am the author.
It is an open source project under the MIT license.
A: A lot of the answers here mention tools that output to ASCII but if you're open to using Unicode then I found this really nice script: https://github.com/Pomax/tex2utf. But do note that from a quick glance over the repository the author doesn't seem keen on maintaining or fixing any issues with this script (who can blame him, it's written in perl).
Example
Input:
g(x) = \int_1^{1/x} \frac{1}{t} f \cdot \left ( \frac{1}{t} \right ) dt

Output:
        ╭ 1/x 1      ╭ 1 ╮
g(x) =  |     ─ f  · │ ─ │ dt
        ╯ 1   t      ╰ t ╯

For comparison:
$$g(x) = \int_1^{1/x} \frac{1}{t} f \cdot \left ( \frac{1}{t} \right ) dt$$
A: At this site one can get following:

Input:

int(int(int(psi^2, x = -inf .. inf), y = -inf .. inf), z = -inf ..
  inf) = 1

Output:
   oo    oo    oo
  /     /     /
 |     |     |    2
 |     |     | psi  dx dy dz = 1
 |     |     |
/     /     /
 -oo   -oo   -oo


Input:

sqrt(e) = 1+1/(1+1/(1+1/(1+1/(5+1/(1+1/(1+1/(9+1/(1+1/(1+...)))))))))

Output:
  _                          1
\/e = 1 + ---------------------------------------
                               1
          1 + -----------------------------------
                                 1
              1 + -------------------------------
                                   1
                  1 + ---------------------------
                                     1
                      5 + -----------------------
                                       1
                          1 + -------------------
                                         1
                              1 + ---------------
                                           1
                                  9 + -----------
                                             1
                                      1 + -------
                                          1 + ...


Input:

e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + ... = 1 + sum(x^n/n!, n = 1
  .. inf)

Output:
                                       oo
              2    3    4             =====  n
 x           x    x    x              \     x
e  = 1 + x + -- + -- + -- + ... = 1 +  >    --
             2!   3!   4!             /     n!
                                      =====
                                      n = 1


Input:

(1/4)pisqrt(2) = sum((-1)^(k+1)/(4*k + 1) + (-1)^(k+1)/(4*k - 3), k
  = 1 .. inf) = 1 + 1/3 - 1/5 - 1/7 + 1/9 + 1/11 - ...

Output:
            oo
           ===== /    k + 1       k + 1\
1 __   _   \     |(-1)        (-1)     |       1   1   1   1    1
- || \/2 =  >    |--------- + ---------| = 1 + - - - - - + - + -- - ...
4          /     \ 4 k + 1     4 k - 3 /       3   5   7   9   11
           =====
           k = 1


Input:

sin(a)/a = cos(a/2) * cos(a/4) * cos(a/8) * cos(a/16) * ... =
  prod(cos(a/2^n), n = 1 .. inf)

Output:
                                        oo
                                       =====
sin a       a     a     a      a        | |       a
----- = cos - cos - cos - cos -- ... =  | |  cos --
  a         2     4     8     16        | |       n
                                        | |      2
                                       n = 1


Input:

lim(1/x^2 - (cos(x)/x)^2, x -> inf) = 1

Output:
        /            2\
        | 1   /cos x\ |
 lim    |-- - |-----| | = 1
        | 2   \  x  / |
x -> oo \x            /


Finally,
$$\int \frac{e^{\sqrt x}}{x^2} \, dx$$
is represented as
Input:

int(e^sqrt(x)/x^2 , x)

Output:
  /
 |    _
 |  \/x
 | e
 | ---- dx
 |   2
 |  x
 |
/

A: I've edited a bit tex2mail to use Unicode for output. Here are the results:
                                      ┌──────┐             
          ┌─┐  3                   4  │     2     6      4             
     ⌠   \│a  x         ┌─┐     3 x  \│1 - x   + x  - 3 x              
     ⎮  ───────── dx = \│a  ──────────────────────────────────         
     ⌡   ┌──────┐                          ┌──────┐         
         │     2            ⎛    2      ⎞  │     2      2         
        \│1 - x             ⎝ 3 x  - 12 ⎠ \│1 - x   - 9x  + 12         

                                 ⎡     1 ⎤n                        
                   lim           ⎢ 1 + ─ ⎥  = e                        
                       n  --> oo ⎣     n ⎦                        

                                     n       n                   
               ⌠1  x     ──┐oo   ⌠1 x (log x)                    
               ⎮  x dx = >       ⎮  ──────────   dx.                   
               ⌡0        ──┘n=0  ⌡0     n!                       


┬─┬oo ⎛   1  ⎞   ⎛ ┬─┬oo   1   ⎞-1           1            1     6 
│ │   ⎜ 1-── ⎟ = ⎜ │ │   ───── ⎟   = ───────────────── = ──── = ──  ≈ 61%
┴ ┴p  ⎜    2 ⎟   ⎜ ┴ ┴p     -2 ⎟         1    1          ζ(2)    2
      ⎝   p  ⎠   ⎝       1-p   ⎠     1 + ── + ── + ∙∙∙          π 
                                          2    2
                                         2    3 

The look depends hugely on the fonts and the browser. If you are interested in the script here is the link.
