Javascript, 978 bytes (824 without CSS)

https://jsfiddle.net/8s37mz1j/

Checklist:

Randomized mine generation - yes
8x8 field with 10 mines - yes
Mine flags - Yes
"unknown" flags - no
Reveal nearby blank spaces when a blank space has been revealed. - yes
Input and output code: It must be playable. - yes

JS:

(function(){
    f=Math.floor;r=Math.random;b=8,s=[-1,0,1],o='',m='*',l=0;

    for(g=[i=b];i;)g[--i]=[0,0,0,0,0,0,0,0];
    for(i=10,a=f(r()*64);i--;g[f(a/b)][a%b]=m)while(g[f(a/b)][a%b])a=f(r()*64);
    for(i=64;i--;z.id='b'+(63-i),c.appendChild(z))z=document.createElement('button');
    for(d=b;d--;)
      for(r=b;r--;)
        s.map(function(y){
          s.map(function(x){
            if(g[d][r]!=m&&g[d+y]&&g[d+y][r+x]==m)g[d][r]++;
          });
        });

    c.onclick=function(e){
        var t=e.target,
            i=t.id.slice(1),
            x=i%b,
            y=f(i/b),
            n=t.className=='b';

      if(t.innerHTML||(n&&!e.ctrlKey))return;
      if(e.ctrlKey)return t.className=(n?'':'b')

      if(q(x,y))alert('boom')
      if(l==54)alert('win')
    };
  function q(x,y){
    if(x<0||x>7||y<0||y>7)return;

    var p=y*b+x,
        v=g[y][x],
        t=document.all['b'+p];

    if(v!=m&&!t.innerHTML){
      t.innerHTML=g[y][x];
      t.className='f';
      l++;
      if(!v){t.className='z';s.map(function(d){s.map(function(r){q(x+r,y+d)})})}
    }
    return v==m
  }
})();

#c{
  width:300px;
  height:300px;
}
button{
  width:12.5%;
  height:12.5%;
  line-height:30px;
}
.f,.z{
  background:#fff;
  border:solid 1px #fff;
}
.z{
  color:#fff;
}
.b{background:#f00}

<div id="c">

MiniJS 812 bytes:

f=Math.floor;r=Math.random;b=8,s=[-1,0,1],o='',m='*',l=0,h='b';for(g=[i=b];i;)g[--i]=[0,0,0,0,0,0,0,0];for(i=10,a=f(r()*64);i--;g[f(a/b)][a%b]=m)while(g[f(a/b)][a%b])a=f(r()*64);for(i=64;i--;z.id=h+(63-i),c.appendChild(z))z=document.createElement('button');for(d=b;d--;)for(r=b;r--;)s.map(function(y){s.map(function(x){if(g[d][r]!=m&&g[d+y]&&g[d+y][r+x]==m)g[d][r]++})});c.onclick=function(e){var t=e.target,i=t.id.slice(1),n=t.className==h;if(t.innerHTML||(n&&!e.ctrlKey))return;if(e.ctrlKey)return t.className=(n?'':h);if(q(i%b,f(i/b)))alert('boom');if(l==54)alert('win')};function q(x,y){if(x<0||x>7||y<0||y>7)return;var p=y*b+x,v=g[y][x],t=document.all[h+p];if(v!=m&&!t.innerHTML){t.innerHTML=g[y][x];t.className='f';l++;if(!v){t.className='z';s.map(function(d){s.map(function(r){q(x+r,y+d)})})}}return v==m}

HTML 12 bytes

<div id="c">

The CSS isn't necessary from a functionality standpoint, but is from a usability standpoint:

#c{
  width:300px;
  height:300px;
}
button{
  width:12.5%;
  height:12.5%;
  line-height:30px;
}
.f,.z{
  background:#fff;
  border:solid 1px #fff;
}
.z{
  color:#fff;
}
.b{background:#f00}

Mini CSS 154 bytes:

#c{width:300px;height:300px}button{width:12.5%;height:12.5%;line-height:30px}.f,.z{background:#fff;border:solid 1px #fff}.z{color:#fff}.b{background:#f00}

Dyalog APL, 113 bytes

{⎕←1 0⍕c+○○h⋄10=+/,h:1⋄m⌷⍨i←⎕:0⋄∇{~⍵⌷h:0⋄(⍵⌷h)←0⋄0=⍵⌷c:∇¨(,⍳⍴m)∩⍵∘+¨,2-⍳3 3⋄0}i}h←=⍨c←{⍉3+/0,⍵,0}⍣2⊢m←8 8⍴10≥?⍨64

non-competing: no "mine" and "unknown" flags

prints * for unopened cells and digits for opened (including 0)

repeatedly asks the user for the 1-based coordinates of a cell to open

ultimately outputs 0 on failure (mine opened) or 1 on success (only 10 unopened left)

looks like this:

********
********
********
********
********
********
********
********
⎕:
      1 1
00000000
11012321
*112****
********
********
********
********
********
⎕:
      3 8
00000000
11012321
*112***1
********
********
********
********
********
⎕:
      4 7
00000000
11012321
*112***1
******3*
********
********
********
********
⎕:

...

Mathematica 566 548 1056

Edit: This is a complete rewrite. I gave up trying to obtain the shortest code and decided instead to build in the features that made most sense.

r indicates the number of rows in the grid. c indicates the number of columns in the grid. m: number of mines.

The game is played by mouse-clicking on the buttons. If the player clicks on a mine, the cell turns black and the program prints "You Lose!"

The checkbox "u" allows the player to peek at the complete solution at any time. The flags, "?" and "!" can be placed in any cell as desired.

DynamicModule[{s, x, f, l},
Manipulate[
Column[{
Grid[s],
If[u, Grid@f, Null]
}],
Grid[{{Control@{{r, 8}, 4, 16, 1, PopupMenu}, 
 Control@{{c, 8}, 4, 16, 1, PopupMenu},
 Control@{{m, 10}, 1, 50, 1, PopupMenu}},
{Button["New", i], 
 Control@{{e, 0}, {0 -> "play", 1 -> "?", 2 -> "!"}, SetterBar}, 
 Control@{{u, False}, {True, False}}}}],
 Deployed -> True,

 Initialization :>
 (p = ReplacePart;
  q = ConstantArray;
  z = Yellow;
  w = White;    
  b := Array[Button["  ", v[{#, #2}], Background -> z] &, {r, c}];
  a := RandomSample[l = Flatten[Array[List, {r, c}], 1], m];
  d[m1_] := 
   p[ListConvolve[BoxMatrix@1, p[q[0, {r, c}], (# -> 1) & /@ m1], 2,
    0], (# -> "*") & /@ (x)];
  n[y_] := Complement[Select[l, ChessboardDistance[y, #] == 1 &], x];
  d[m1_] := 
  p[ListConvolve[BoxMatrix@1, p[q[0, {r, c}], (# -> 1) & /@ m1], 2,
    0], (# -> "*") & /@ (x)];

  v[{r_, c_}] :=
   Switch[e,
    1, If[s[[r, c, 3, 2]] == z, 
     s = p[s, {{r, c, 1} -> If[s[[r, c, 1]] == "?", "  ", "?"]}], 
     Null],
  
    2, If[s[[r, c, 3, 2]] == z, 
    s = p[s, {{r, c, 1} -> If[s[[r, c, 1]] == "!", "  ", "!"]}], 
    Null],
    3, Null,
  
  
    0, Switch[f[[r, c]],
     "*", (Print["You lose!"]; (s = p[s, {r, c, 3, 2} -> Black])),
     0, (s = p[s, {{r, c, 1} -> "  ", {r, c, 3, 2} -> w}]; 
      f = p[f, {{r, c} -> ""}]; v /@ n[{r, c}]),
     "  ", Null,
     _, (s = p[s, {{r, c, 1} -> f[[r, c]], {r, c, 3, 2} -> w}])]];
  
   i :=
   (x = a;s = b;f = d[x]);i) ] ]

Initial State

At a later point...

Python 2.7 (487C)

"""
char meaning:
    '?': unknown flag
    '!': mine flag
    'x': default
how to play:
    Input 3 chars each time. The first char is the action
    and the rest form a position. For example, '013' means
    uncover grid (1,3), '110' means flag the grid (1,0).

    The top-left corner is (0, 0), bottom-left (7,0), etc.

    Player will lose after uncover a mine, the program will 
    output "Bom". If the Player uncovers all grid that do 
    not contain a mine, he wins and the program will output 
    "Win".
"""
import random as Z
S=sum
M=map
T=range
P=[(i,j)for i in T(8)for j in T(8)]
C=dict(zip(T(-3,9),'?!x012345678'))
m={p:-1 for p in P}
h=Z.sample(P,10)
def U(p):
 if m[p]>=0:return 0
 n=filter(lambda(c,d):0<max(abs(p[0]-c),abs(p[1]-d))<2,P)
 m[p]=s=S((x in h)for x in n)
 return(1 if s else S(M(U,n))+1,-1)[p in h]
s=u=0
while(s<54)&(u>-1):
 f,i,j=M(int,raw_input(''.join((C[m[x]]+'\n '[x[1]<7])for x in P)))
 p=i,j;c=m[p]
 if f*(c<0):m[p]=-1-(-c)%3
 else:u=U(p);s+=u
print'WBionm'[s<54::2]

Full game experience:

x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
000
0 0 1 x x x x x
0 0 2 x x x x x
0 0 2 x x x x x
0 0 1 2 x x x x
0 0 0 1 x x x x
1 1 0 2 x x x x
x 1 0 2 x x x x
x 1 0 1 x x x x
070
0 0 1 x x x x x
0 0 2 x x x x x
0 0 2 x x x x x
0 0 1 2 x x x x
0 0 0 1 x x x x
1 1 0 2 x x x x
x 1 0 2 x x x x
1 1 0 1 x x x x
123
0 0 1 x x x x x
0 0 2 x x x x x
0 0 2 ! x x x x
0 0 1 2 x x x x
0 0 0 1 x x x x
1 1 0 2 x x x x
x 1 0 2 x x x x
1 1 0 1 x x x x
113
0 0 1 x x x x x
0 0 2 ! x x x x
0 0 2 ! x x x x
0 0 1 2 x x x x
0 0 0 1 x x x x
1 1 0 2 x x x x
x 1 0 2 x x x x
1 1 0 1 x x x x
003
0 0 1 1 x x x x
0 0 2 ! x x x x
0 0 2 ! x x x x
0 0 1 2 x x x x
0 0 0 1 x x x x
1 1 0 2 x x x x
x 1 0 2 x x x x
1 1 0 1 x x x x
004
0 0 1 1 1 x x x
0 0 2 ! x x x x
0 0 2 ! x x x x
0 0 1 2 x x x x
0 0 0 1 x x x x
1 1 0 2 x x x x
x 1 0 2 x x x x
1 1 0 1 x x x x
014
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! x x x x
0 0 1 2 x x x x
0 0 0 1 x x x x
1 1 0 2 x x x x
x 1 0 2 x x x x
1 1 0 1 x x x x
154
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! x x x x
0 0 1 2 x x x x
0 0 0 1 x x x x
1 1 0 2 ! x x x
x 1 0 2 x x x x
1 1 0 1 x x x x
044
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! x x x x
0 0 1 2 x x x x
0 0 0 1 1 x x x
1 1 0 2 ! x x x
x 1 0 2 x x x x
1 1 0 1 x x x x
034
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! x x x x
0 0 1 2 3 x x x
0 0 0 1 1 x x x
1 1 0 2 ! x x x
x 1 0 2 x x x x
1 1 0 1 x x x x
035
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! x x x x
0 0 1 2 3 3 x x
0 0 0 1 1 x x x
1 1 0 2 ! x x x
x 1 0 2 x x x x
1 1 0 1 x x x x
045
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! x x x x
0 0 1 2 3 3 x x
0 0 0 1 1 1 x x
1 1 0 2 ! x x x
x 1 0 2 x x x x
1 1 0 1 x x x x
055
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! x x x x
0 0 1 2 3 3 x x
0 0 0 1 1 1 x x
1 1 0 2 ! 2 x x
x 1 0 2 x x x x
1 1 0 1 x x x x
124
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! ! x x x
0 0 1 2 3 3 x x
0 0 0 1 1 1 x x
1 1 0 2 ! 2 x x
x 1 0 2 x x x x
1 1 0 1 x x x x
164
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! ! x x x
0 0 1 2 3 3 x x
0 0 0 1 1 1 x x
1 1 0 2 ! 2 x x
x 1 0 2 ! x x x
1 1 0 1 x x x x
174
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! ! x x x
0 0 1 2 3 3 x x
0 0 0 1 1 1 x x
1 1 0 2 ! 2 x x
x 1 0 2 ! x x x
1 1 0 1 ! x x x
074
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! ! x x x
0 0 1 2 3 3 x x
0 0 0 1 1 1 x x
1 1 0 2 ! 2 x x
x 1 0 2 ! x x x
1 1 0 1 1 x x x
125
0 0 1 1 1 x x x
0 0 2 ! 4 x x x
0 0 2 ! ! ! x x
0 0 1 2 3 3 x x
0 0 0 1 1 1 x x
1 1 0 2 ! 2 x x
x 1 0 2 ! x x x
1 1 0 1 1 x x x
005
0 0 1 1 1 1 x x
0 0 2 ! 4 x x x
0 0 2 ! ! ! x x
0 0 1 2 3 3 x x
0 0 0 1 1 1 x x
1 1 0 2 ! 2 x x
x 1 0 2 ! x x x
1 1 0 1 1 x x x
015
0 0 1 1 1 1 x x
0 0 2 ! 4 4 x x
0 0 2 ! ! ! x x
0 0 1 2 3 3 x x
0 0 0 1 1 1 x x
1 1 0 2 ! 2 x x
x 1 0 2 ! x x x
1 1 0 1 1 x x x
126
0 0 1 1 1 1 x x
0 0 2 ! 4 4 x x
0 0 2 ! ! ! ! x
0 0 1 2 3 3 x x
0 0 0 1 1 1 x x
1 1 0 2 ! 2 x x
x 1 0 2 ! x x x
1 1 0 1 1 x x x
036
0 0 1 1 1 1 x x
0 0 2 ! 4 4 x x
0 0 2 ! ! ! ! x
0 0 1 2 3 3 3 x
0 0 0 1 1 1 x x
1 1 0 2 ! 2 x x
x 1 0 2 ! x x x
1 1 0 1 1 x x x
046
0 0 1 1 1 1 x x
0 0 2 ! 4 4 x x
0 0 2 ! ! ! ! x
0 0 1 2 3 3 3 2
0 0 0 1 1 1 0 0
1 1 0 2 ! 2 0 0
x 1 0 2 ! 2 0 0
1 1 0 1 1 1 0 0
127
0 0 1 1 1 1 x x
0 0 2 ! 4 4 x x
0 0 2 ! ! ! ! !
0 0 1 2 3 3 3 2
0 0 0 1 1 1 0 0
1 1 0 2 ! 2 0 0
x 1 0 2 ! 2 0 0
1 1 0 1 1 1 0 0
007
0 0 1 1 1 1 x 1
0 0 2 ! 4 4 x x
0 0 2 ! ! ! ! !
0 0 1 2 3 3 3 2
0 0 0 1 1 1 0 0
1 1 0 2 ! 2 0 0
x 1 0 2 ! 2 0 0
1 1 0 1 1 1 0 0
017
0 0 1 1 1 1 x 1
0 0 2 ! 4 4 x 3
0 0 2 ! ! ! ! !
0 0 1 2 3 3 3 2
0 0 0 1 1 1 0 0
1 1 0 2 ! 2 0 0
x 1 0 2 ! 2 0 0
1 1 0 1 1 1 0 0
016
Win

The last step is dangerous, though.

C, 568, 557, 537

Checklist:
  Randomized mine generation - yes
  8x8 field with 10 mines - yes
  Mine and "unknown" flags - yes
  Reveal nearby blank spaces when a blank space has been revealed. - yes
  Input and output code: It must be playable. - yes

Further to playable: 
  Win detection (found all mines, or revealed all empties)
  Bang detection (hit a mine)
  Game terminates.

Output format:
  # - unrevealed
  ! - a flagged mine
  * - a mine
  (number) - number of neighbouring mines
  ? - unknown flag

Input format:
  x y f 
  - where x is 0..7, y is 0..7 (origin upper-left)
  - f is 0 to open up, 1 to flag a mine, and 2 to flag a unknown

example game:

./a.out
5 5 0
# 1 0 0 0 2 # #
# 1 0 0 0 2 # #
# 1 0 0 0 1 1 1
# 1 0 0 0 0 0 0
# # 1 0 0 0 1 1
# # 1 0 0 0 1 #
# # # 1 2 1 # #
# # # # # # # #
6 1 1
# 1 0 0 0 2 # #
# 1 0 0 0 2 ! #
# 1 0 0 0 1 1 1
# 1 0 0 0 0 0 0
# # 1 0 0 0 1 1
# # 1 0 0 0 1 #
# # # 1 2 1 # #
# # # # # # # #
7 5 0
# 1 0 0 0 2 # #
# 1 0 0 0 2 ! #
# 1 0 0 0 1 1 1
# 1 0 0 0 0 0 0
# # 1 0 0 0 1 1
# # 1 0 0 0 1 *
# # # 1 2 1 # 1
# # # # # # # #
bang!

code:

// 8x8 grid but with padding before first row, after last row, and after last column, i.e. its 9x10
m[99]; // 0=empty,1=mine
u[99]; // 0=revealed,1=unrevealed,2=flag,3=unknown

// count neighbouring mines (8way)
c(i){return m[i-8]+m[i-9]+m[i-10]+m[i+8]+m[i+9]+m[i+10]+m[i-1]+m[i+1];}

// reveal (4way)
r(i){
    if(u[i]){
        u[i]=0;
        if(!c(i))r(i-9),r(i+9),r(i+1),r(i-1);
    }
}

i,x,y,f,e;
main(){
    // place 10 mines
    for(srand(time(0));i<10;){
        x=rand()%64;
        x+=9+x/8;
        if(!m[x]){
            m[x]=1;
            i++;
        }
    }
    for(;y<64;y++)u[y+9+y/8]=1; // mark visible grid as being unrevealed

    while(!e){
        // read input 0..7 0..7 0..2
        scanf("%d%d%d",&x,&y,&f);
        i=x+9+y*9;
        if(f)u[i]=f==1?2:u[i]==3?1:3;else r(i); // flag, toggle unknown/unrevealed, open

        // show grid and calc score
        for(y=f=x=0;x<64;x++){
            i=x+9+x/8;
            putchar(u[i]?" #!?"[u[i]]:m[i]?42:48+c(i)); // 42='*', 48='0'
            putchar(x%8==7?10:32);
            if(!u[i])y+=m[i]?-99:1;   // y = number of correctly open
            if(u[i]==2)f+=m[i]?1:-99; // f = number of correct mines
        }
        if(y<0||y==54||f==10)e=puts(y<0?"bang!":"win!"); // 54 = 64-10
    }
}

Python (502 566)

Checklist:

Randomized mine generation - yes
8x8 field with 10 mines - yes
Mine and "unknown" flags - yes
Reveal nearby blank spaces when a blank space has been revealed. - yes
Input and output code: It must be playable. - yes

It has a win detector as well.

Input is given while the game is running, with (f, x, y). (x, y) is the coordinates of the grid selection, f is whether you want to flag or not. (0, 0, 0) would open up (0, 0), and (1, 2, 3) would flag (2, 3). Flagging works in a cycle: flagging a square twice gives a question mark.

(number) - number of mines
(space) - unexplored
. - 0 mines
! - flag
" - question

import random
A=[-1,0,1]
R=lambda x:[x+i for i in[-9,-8,-7,-1,1,7,8,9]if(0<x+i<64)&([i,x%8]not in([7,0],[-7,7],[-1,0],[1,7]))]
M=lambda p:sum(G[i]=='*'for i in R(p))
def V(p):
 m=M(p);G[p]=`m`if m else'.'
 if m>0:return
 for c in R(p):
  if' '!=G[c]:continue
  m=M(c);G[c]=`m`
  if m==0:G[c]='.';V(c)
G=[' ']*54+['*']*10
random.shuffle(G)
while' 'in`G`:
 for i in range(8):print[j.replace('*',' ')[0]for j in G[8*i:8*i+8]]
 i=input()[::-1];a=i[0]*8+i[1];b=G[a]
 if i[2]:G[a]=(chr(ord(b[0])+1)if'"'!=b[0]else' ')+b[1:];continue
 if'*'==b:print'L';break
 if'!'!=b:V(a)

Needs to be improved: function R [get all squares around item p] (101 chars), printing (69 chars), flagging (72 chars)