PHP - 68 (or 39) bytes

<?foreach(count_chars(fgets(STDIN),1)as$k=>$v)echo chr($k)." : $v
";

Output for the example text:

  : 15
. : 1
T : 1
a : 10
c : 1
d : 4
e : 8
f : 2
g : 3
h : 3
i : 10
m : 1
n : 10
o : 4
p : 3
q : 1
r : 2
s : 5
t : 6
u : 1
x : 1
y : 1

If the exact output is not required, this would work for 39 bytes:

<?print_r(count_chars(fgets(STDIN),1));

Sample output:

Array
(
    [32] => 15
    [46] => 1
    [84] => 1
    [97] => 10
    [99] => 1
    [100] => 4
    [101] => 8
    [102] => 2
    [103] => 3
    [104] => 3
    [105] => 10
    [109] => 1
    [110] => 10
    [111] => 4
    [112] => 3
    [113] => 1
    [114] => 2
    [115] => 5
    [116] => 6
    [117] => 1
    [120] => 1
    [121] => 1
)

where each numerical index refers the ordinal value of the character it represents.

I suspect very strongly that using an in-built function that does exactly what the problem states will soon be disallowed.

GNU core utils - 29 22 20 chars (53 with formatting)

Wumpus's improvement (20 chars):

fold -1|sort|uniq -c

Firefly's improvement (22 chars):

grep -o .|sort|uniq -c

joeytwiddle's original (29 chars):

sed 's+.+\0\n+g'|sort|uniq -c

Originally I used sed to simply add a newline after each character. Firefly improved on that with grep -o ., since -o displays every matched pattern on its own line. Wumpus pointed out a further improvement using fold -1 instead. Nice work!

uniq does the real work, although it only applies to sorted lists.

Note that the output format does not exactly match the example in the question. That requires a final run through sed to swap the arguments. (Waiting on an answer to Jan Dvorak's question to see if this is required...)

Reformatting with sed is "only" another 33 characters! (Total 53)

|sed 's/ *\(.*\) \(.\)/\2 :  \1/'

Awk can almost do the job whilst adding only 25 chars, but it hides the first space. Silly awk!

|awk '{print $2" :  "$1}'

I wonder if improvements can be made in the reformatting stage...

k (8 7)

#:'=0:0

Example

k)#:'=:0:0
The definition of insanity is quoting the same phrase again and again and not expect despair.
T| 1
h| 3
e| 8
 | 15
d| 4
f| 2
i| 10
n| 10
t| 6
o| 4
s| 5
a| 10
y| 1
q| 1
u| 1
g| 3
m| 1
p| 3
r| 2
x| 1
c| 1
.| 1

edit: Down to seven, H/T Aaron Davies

Ruby 1.9.3: 53 characters

(Based on @shiva's and @daneiro's comments.)

gets.split("").uniq.map{|x|puts x+" : #{$_.count x}"}

Sample run:

bash-4.1$ ruby -e 'a=gets;a.split("").uniq.map{|x|puts"#{x} : #{a.count x}"}' <<< 'Hello world'
H : 1
e : 1
l : 3
o : 2
  : 1
w : 1
r : 1
d : 1

 : 1

Ruby: 44 characters

Not respecting the output format:

s=Hash.new 0;gets.chars{|c|s[c]+=1};pp s

Sample run:

bash-4.1$ ruby -rpp -e 's=Hash.new 0;gets.chars{|c|s[c]+=1};pp s' <<< 'Hello, world!'
{"H"=>1,
 "e"=>1,
 "l"=>3,
 "o"=>2,
 ","=>1,
 " "=>1,
 "w"=>1,
 "r"=>1,
 "d"=>1,
 "!"=>1,
 "\n"=>1}

Python 3: 76 characters

76

import collections as c
for x,y in c.Counter(input()).items():print(x,':',y)

44

(print same characters many times, see Wasi's answer for a valid version)

a=input()
for x in a:print(x,':',a.count(x))

Python 2, correctly (58)

s=raw_input()
for l in set(s):print l+" : "+str(s.count(l))

Output:

python count.py
The definition of insanity is quoting the same phrase again and again and not expect despair.
  : 15
. : 1
T : 1
a : 10
c : 1
e : 8
d : 4
g : 3
f : 2
i : 10
h : 3
m : 1
o : 4
n : 10
q : 1
p : 3
s : 5
r : 2
u : 1
t : 6
y : 1
x : 1

Python 2, cheetah style (41)

s=input()
print {l:s.count(l) for l in s}

Output:

python count.py
"The definition of insanity is quoting the same phrase again and again and not expect despair."
{' ': 15, '.': 1, 'T': 1, 'a': 10, 'c': 1, 'e': 8, 'd': 4, 'g': 3, 'f': 2, 'i': 10, 'h': 3, 'm': 1, 'o': 4, 'n': 10, 'q': 1, 'p': 3, 's': 5, 'r': 2, 'u': 1, 't': 6, 'y': 1, 'x': 1}

Perl 6: 21 chars

.say for get.comb.Bag

(REPL)
> .say for get.comb.Bag
The definition of insanity is quoting the same phrase again and again and not expect despair.
"T" => 1
"h" => 3
"e" => 8
" " => 15
"d" => 4
"f" => 2
"i" => 10
"n" => 10
"t" => 6
"o" => 4
"s" => 5
"a" => 10
"y" => 1
"q" => 1
"u" => 1
"g" => 3
"m" => 1
"p" => 3
"r" => 2
"x" => 1
"c" => 1
"." => 1

APL (15)

M,⍪+⌿Z∘.=M←∪Z←⍞

If you really need the :, it's 19 (but there's others who aren't including it):

M,':',⍪+⌿Z∘.=M←∪Z←⍞

Output:

      M,⍪+⌿Z∘.=M←∪Z←⍞
The definition of insanity is quoting the same phrase again and again and not expect despair. 
T  1
h  3
e  8
  16
d  4
f  2
i 10
n 10
t  6
o  4
s  5
a 10
y  1
q  1
u  1
g  3
m  1
p  3
r  2
x  1
c  1
.  1

Perl 5, 54 characters

map{$h{$_}++}split//,<>;print"$_ : $h{$_}\n"for keys%h

JavaScript (44 characters):

Expects s to hold a string value.

r={};[].map.call(s,function(e){r[e]=-~r[e]})

The output is contained in r.

R, 30 characters

table(strsplit(readline(),""))

Example usage:

> table(strsplit(readline(),""))
The definition of insanity is quoting the same phrase again and again and not expect despair.

    .  a  c  d  e  f  g  h  i  m  n  o  p  q  r  s  t  T  u  x  y 
15  1 10  1  4  8  2  3  3 10  1 10  4  3  1  2  5  6  1  1  1  1 

python 3, 49

Stealing idea from evuez

t=input()
for i in set(t):print(i,':',t.count(i))

input:

The definition of insanity is quoting the same phrase again and again and not expect despair.

output:

  :  15
. :  1
T :  1
a :  10
c :  1
e :  8
d :  4
g :  3
f :  2
i :  10
h :  3
m :  1
o :  4
n :  10
q :  1
p :  3
s :  5
r :  2
u :  1
t :  6
y :  1
x :  1

C# (220 chars)

Line breaks added for readability, my first feeble attempt at code golf! :)

class P {static void Main(){var d=new Dictionary<char,int>();
Console.ReadLine().ToList().ForEach(x=>{ if(d.ContainsKey(x))
{d[x]++;}else{d.Add(x,1);}});Console.WriteLine(string
.Join("\n",d.Keys.Select(x=>x+":" +d[x])));}}

Powershell, 63

$a=@{};[char[]](read-host)|%{$a[$_]++};$a.Keys|%{"$_ :"+$a[$_]}

J, 22 characters

(~.;"0+/@(=/~.))1!:1]1

Example:

   (~.;"0+/@(=/~.))1!:1]1
The definition of insanity is quoting the same phrase again and again and not expect despair.
+-+--+
|T|1 |
+-+--+
|h|3 |
+-+--+
|e|8 |
+-+--+
| |15|
+-+--+
|d|4 |
+-+--+
|f|2 |
+-+--+
|i|10|
+-+--+
|n|10|
+-+--+
|t|6 |
+-+--+
|o|4 |
+-+--+
|s|5 |
+-+--+
|a|10|
+-+--+
|y|1 |
+-+--+
|q|1 |
+-+--+
|u|1 |
+-+--+
|g|3 |
+-+--+
|m|1 |
+-+--+
|p|3 |
+-+--+
|r|2 |
+-+--+
|x|1 |
+-+--+
|c|1 |
+-+--+
|.|1 |
+-+--+

JavaScript

1. 66 53 bytes:

   prompt(a={}).replace(/./g,function(c){a[c]=-~a[c]}),a
   

2. 69 56 bytes:

   b=prompt(a={});for(i=b.length;i--;){a[b[i]]=-~a[b[i]]};a
   

3. 78 65 bytes:

   prompt().split('').reduce(function(a,b){return a[b]=-~a[b],a},{})
   

N.B.: In all cases deleted number of bytes refer to extra console.log() call which is pointless if run in the console. Big thanks to @imma for the great catch with -~a[b] and prompt(a={}). This definitely saved some more bytes.

C#: 129

This is Avivs answer but shorter:

var s=Console.ReadLine();for(int i=0;i<256;i++){var ch=(char)i;Console.Write(s.Contains(ch)?ch+":"+s.Count(c=>c==ch)+"\r\n":"");}

This is mine:

C#: 103

foreach(var g in Console.ReadLine().OrderBy(o=>o).GroupBy(c=>c))Console.WriteLine(g.Key+":"+g.Count());

Bash (20 characters)

 ptx -S.|sort|uniq -c
 10                                        a
  1                                        c
  4                                        d
  8                                        e
  2                                        f
  3                                        g
  3                                        h
 10                                        i
  1                                        m
 10                                        n
  4                                        o
  3                                        p
  1                                        q
  2                                        r
  5                                        s
  6                                        t
  1                                        T
  1                                        u
  1                                        x
  1                                        y

ASCII encoding now supported

Bash (23 characters):

xxd -p -c1|sort|uniq -c

  1 0a
 15 20
  1 2e
  1 54
 10 61
  1 63
  4 64
  8 65
  2 66
  3 67
  3 68
 10 69
  1 6d
 10 6e
  4 6f
  3 70
  1 71
  2 72
  5 73
  6 74
  1 75
  1 78
  1 79

ASCII formatting not supported

Befunge 98 - 31 to 42 chars

This does not print the spaces, and only prints for characters in the string (once for each character, even duplicates). So an input of aa will produce an output of:

a:2
a:2

31 chars

~::1g1+\1p;,a.- 'g1,:',:@j`0:;#

The following seems to match almost exactly. It outputs only one time for each character, in the order they appear in the string. An input of Bbaa gives an output of

B:1
b:1
a:2

38 chars

~:1g' `j::1g1+\1p;,a.- 'g1,:',:@j`0:;#

The following prints the spaces exactly as in the output example. It also outputs every single ascii character's count, which, since it is not clearly specified, I'll say is valid.

42 chars

~:1g1+\1p;,a+1.- 'g1:,,:,," : ",:@j!`~':;#

Windows Command Script - 72 Bytes

set/p.=
:a
set/a\%.:~,1%=\%.:~,1%+1
set.=%.:~1%
%.%goto:b
goto:a
:b
set\

Outputs:

\=15 (space)
\.=1
\a=10
\c=1
\d=4
\e=8
\f=2
\g=3
\h=3
\i=10
\m=1
\n=10
\o=4
\p=3
\q=1
\r=2
\s=5
\T=7
\u=1
\x=1
\y=1

J, 23 chars

(~.;"0+/@|:@=)/:~1!:1]1

Slightly different output format (line 2 is stdin):

   (~.;"0+/@|:@=)/:~1!:1]1
Mississippi
┌─┬─┐
│M│1│
├─┼─┤
│i│4│
├─┼─┤
│p│2│
├─┼─┤
│s│4│
└─┴─┘

Haskell, 93

import Data.List
main=getLine>>=mapM(\s->putStrLn$[head s]++" : "++show(length s)).group.sort

C#

string str = Console.ReadLine(); // Get Input From User Here
char chr;
for (int i = 0; i < 256; i++)
{
    chr = (char)i; // Use The Integer Index As ASCII Char Value --> Convert To Char
    if (str.IndexOf(chr) != -1) // If The Current Char Exists In The Input String
    {
        Console.WriteLine(chr + " : " + str.Count(x => x == chr)); // Count And Display
    }
}
Console.ReadLine(); // Hold The Program Open.

In Our Case, If The Input Will Be "The definition of insanity is quoting the same phrase again and again and not expect despair."

The Output Will Be:

  : 15
. : 1
T : 1
a : 10
c : 1
d : 4
e : 8
f : 2
g : 3
h : 3
i : 10
m : 1
n : 10
o : 4
p : 3
q : 1
r : 2
s : 5
t : 6
u : 1
x : 1
y : 1

F# (66 59, 82 with prescribed formattting)

let f s=s|>Seq.sort|>Seq.countBy(id)|>Seq.iter(printfn"%A")

Output:

> f The definition of insanity is quoting the same phrase again and again and not expect despair.
(' ', 15)
('.', 1)
('T', 1)
('a', 10)
('c', 1)
('d', 4)
('e', 8)
('f', 2)
('g', 3)
('h', 3)
('i', 10)
('m', 1)
('n', 10)
('o', 4)
('p', 3)
('q', 1)
('r', 2)
('s', 5)
('t', 6)
('u', 1)
('x', 1)
('y', 1)

With the prescribed formatting, it becomes:

let f s=s|>Seq.sort|>Seq.countBy(id)|>Seq.iter(fun(a,b)->printfn"\"%c\" :  %d"a b)

Python 2 (90 chars)

import collections as c;print"\n".join("%s %s"%i for i in c.Counter(raw_input()).items())

Output when run on its own source:

  8
" 4
% 3
) 4
( 4
. 3
; 1
C 1
\ 1
_ 1
a 2
c 4
e 3
f 1
i 9
j 1
m 2
l 2
o 6
n 7
p 3
s 5
r 5
u 2
t 6
w 1

PowerShell (49)

[char[]](read-host)|group|%{$_.Name+":"+$_.Count}

Mathematica, 61 bytes

Map[{#[[1]], Length@#} &, Gather@Characters[Input[]]] // TableForm

It then pops up this dialog box,

and for the sample sentence, produces as output