There's an experimental CSS property called text-stroke, supported on some browsers behind a -webkit prefix.

h1 { -webkit-text-stroke: 2px black; /* width and color */ font-family: sans; color: yellow; }

Hello World

Another possible trick would be to use four shadows, one pixel each on all directions, using property text-shadow:

h1 { /* 1 pixel black shadow to left, top, right and bottom */ text-shadow: -1px 0 black, 0 1px black, 1px 0 black, 0 -1px black; font-family: sans; color: yellow; }

Hello World

But it would get blurred for more than 1 pixel thickness.

UPDATE

Here's a SCSS mixin to generate the stroke: http://codepen.io/pixelass/pen/gbGZYL

/// Stroke font-character
/// @param  {Integer} $stroke - Stroke width
/// @param  {Color}   $color  - Stroke color
/// @return {List}            - text-shadow list
@function stroke($stroke, $color) {
  $shadow: ();
  $from: $stroke*-1;
  @for $i from $from through $stroke {
   @for $j from $from through $stroke {
      $shadow: append($shadow, $i*1px $j*1px 0 $color, comma);
    }
  }
  @return $shadow;
}
/// Stroke font-character
/// @param  {Integer} $stroke - Stroke width
/// @param  {Color}   $color  - Stroke color
/// @return {Style}           - text-shadow
@mixin stroke($stroke, $color) {
  text-shadow: stroke($stroke, $color);
}

https://i.stack.imgur.com/btzoG.png

YES old question.. with accepted (and good) answers..

BUT...In case anybody ever needs this and hates typing code...

THIS is a 2px black border with CrossBrowser support (not IE) I needed this for @fontface fonts so it needed to be cleaner than previous seen answers... I takes every side pixelwise to make sure there are (almost) no gaps for "fuzzy" (handrawn or similar) fonts. Subpixels (0.5px) could be added but I don't need it.

Long code for just the border??? ...YES!!!

text-shadow: 1px 1px 0 #000,
    -1px 1px 0 #000,
    1px -1px 0 #000,
    -1px -1px 0 #000,
    0px 1px 0 #000,
    0px -1px 0 #000,
    -1px 0px 0 #000,
    1px 0px 0 #000,
    2px 2px 0 #000,
    -2px 2px 0 #000,
    2px -2px 0 #000,
    -2px -2px 0 #000,
    0px 2px 0 #000,
    0px -2px 0 #000,
    -2px 0px 0 #000,
    2px 0px 0 #000,
    1px 2px 0 #000,
    -1px 2px 0 #000,
    1px -2px 0 #000,
    -1px -2px 0 #000,
    2px 1px 0 #000,
    -2px 1px 0 #000,
    2px -1px 0 #000,
    -2px -1px 0 #000;

You could perhaps emulate a text-stroke, using the css text-shadow (or -webkit-text-shadow/-moz-text-shadow) and a very low blur:

#element
{
  text-shadow: 0 0 2px #000; /* horizontal-offset vertical-offset 'blur' colour */
  -moz-text-shadow: 0 0 2px #000;
  -webkit-text-shadow: 0 0 2px #000;
}

But while this is more widely available than the -webkit-text-stroke property, I doubt that it's available to the majority of your users, but that might not be a problem (graceful degradation, and all that).

To elaborate more on some answers that have mentioned -webkit-text-stroke, here's is the code to make it work:

div {
  -webkit-text-fill-color: black;
  -webkit-text-stroke-color: red;
  -webkit-text-stroke-width: 2.00px; 
}

An in-depth article about using text stroke is here and a list of browsers that support text stroke is here.

There seems to be a 'text-stroke' property, but (at least for me) it only works in Safari.

http://webkit.org/blog/85/introducing-text-stroke/

Here's what I'm using :

.text_with_1px_border
{
    text-shadow: 
        -1px -1px 0px #000,
         0px -1px 0px #000,
         1px -1px 0px #000,
        -1px  0px 0px #000,
         1px  0px 0px #000,
        -1px  1px 0px #000,
         0px  1px 0px #000,
         1px  1px 0px #000;
}

.text_with_2px_border
{
    text-shadow: 
        /* first layer at 1px */
        -1px -1px 0px #000,
         0px -1px 0px #000,
         1px -1px 0px #000,
        -1px  0px 0px #000,
         1px  0px 0px #000,
        -1px  1px 0px #000,
         0px  1px 0px #000,
         1px  1px 0px #000,
        /* second layer at 2px */
        -2px -2px 0px #000,
        -1px -2px 0px #000,
         0px -2px 0px #000,
         1px -2px 0px #000,
         2px -2px 0px #000,
         2px -1px 0px #000,
         2px  0px 0px #000,
         2px  1px 0px #000,
         2px  2px 0px #000,
         1px  2px 0px #000,
         0px  2px 0px #000,
        -1px  2px 0px #000,
        -2px  2px 0px #000,
        -2px  1px 0px #000,
        -2px  0px 0px #000,
        -2px -1px 0px #000;
}

Sorry I'm late, but speaking about text-shadow, I thought you would also like this example (I use it quite often when I need good shadows on text):

text-shadow:
    -2px   -2px lightblue,
    -2px -1.5px lightblue,
    -2px   -1px lightblue,
    -2px -0.5px lightblue,
    -2px    0px lightblue,
    -2px  0.5px lightblue,
    -2px    1px lightblue,
    -2px  1.5px lightblue,
    -2px    2px lightblue,
    -1.5px  2px lightblue,
    -1px    2px lightblue,
    -0.5px  2px lightblue,
    0px     2px lightblue,
    0.5px   2px lightblue,
    1px     2px lightblue,
    1.5px   2px lightblue,
    2px     2px lightblue,
    2px   1.5px lightblue,
    2px     1px lightblue,
    2px   0.5px lightblue,
    2px     0px lightblue,
    2px  -0.5px lightblue,
    2px    -1px lightblue,
    2px  -1.5px lightblue,
    2px    -2px lightblue,
    1.5px  -2px lightblue,
    1px    -2px lightblue,
    0.5px  -2px lightblue,
    0px    -2px lightblue,
    -0.5px -2px lightblue,
    -1px   -2px lightblue,
    -1.5px -2px lightblue;

Since webkit seems to bug around for me, I wasn't satisfied with the answers. Then I found this codepen which can generate raw CSS for you. Just type in the color and border width in the JS and scroll down to the CSS output.

Example of 2px black text outline:

  text-shadow: -2px -2px 0 black,-2px -1px 0 black,-2px 0px 0 black,-2px 1px 0 black,-2px 2px 0 black,-1px -2px 0 black,-1px -1px 0 black,-1px 0px 0 black,-1px 1px 0 black,-1px 2px 0 black,0px -2px 0 black,0px -1px 0 black,0px 0px 0 black,0px 1px 0 black,0px 2px 0 black,1px -2px 0 black,1px -1px 0 black,1px 0px 0 black,1px 1px 0 black,1px 2px 0 black,2px -2px 0 black,2px -1px 0 black,2px 0px 0 black,2px 1px 0 black,2px 2px 0 black

Just in case the codepen gets removed (Vue.js):

new Vue({
  el: '#app',
  data: {
    width: 5,
    color: 'DeepPink',
    styles: ''
  },
  
  created() {
    this.textChange()
  },
  
  methods: {
    textChange() {
      var shadows = []
      var color = this.color
      
      for(let i = -this.width; i <= this.width; i++) {
        for(let j = -this.width; j <= this.width; j++) {
          shadows.push(`${i*1}px ${j*1}px 0 ${color}`)
        }
      }
      
      this.styles = shadows.join(',')
    }
  }
})

html:

<p><strong>text-shadow:</strong> {{styles}}</p>

text-shadow:
    1px  1px 2px black,
    1px -1px 2px black,
   -1px  1px 2px black,
   -1px -1px 2px black;

Stroke font-character with a Less mixin

Here's a LESS mixin to generate the stroke: http://codepen.io/anon/pen/BNYGBy?editors=110

/// Stroke font-character
/// @param  {Integer} $stroke - Stroke width
/// @param  {Color}   $color  - Stroke color
/// @return {List}            - text-shadow list
.stroke(@stroke, @color) {
  @maxi: @stroke + 1;
  .i-loop (@i) when (@i > 0) {
    @maxj: @stroke + 1;
    .j-loop (@j) when (@j > 0) {
      text-shadow+: (@i - 1)*(1px)  (@j - 1)*(1px) 0 @color;
      text-shadow+: (@i - 1)*(1px)  (@j - 1)*(-1px) 0 @color;
      text-shadow+: (@i - 1)*(-1px)  (@j - 1)*(-1px) 0 @color;
      text-shadow+: (@i - 1)*(-1px)  (@j - 1)*(1px) 0 @color;
      .j-loop(@j - 1);
    }
    .j-loop (0) {}
    .j-loop(@maxj);
    .i-loop(@i - 1);
  }
  .i-loop (0) {}
  .i-loop(@maxi);
  text-shadow+: 0 0 0 @color;
}

(it's based on pixelass answer that instead uses SCSS)

I created a comparison of all the solutions mentioned here to have a quick overview:

<h1>with mixin</h1>
<h2>with text-shadow</h2>
<h3>with css text-stroke-width</h3>

https://codepen.io/Grienauer/pen/GRRdRJr

I once tried to do those round corners and drop shadows with css3. Later on, I found it is still poorly supported (Internet Explorer(s), of course!)

I ended up trying to do that in JS (HTML canvas with IE Canvas), but it impacts the performance a lot (even on my C2D machine). In short, if you really need the effect, consider JS libraries (most of them should be able to run on IE6) but don't over do it due to performance issues; if you still need an alternative... you could use SFiR, then PS it and SFiR it. CSS3 isn't ready today.