How to remove unwanted space between rows and columns in table?

Add this CSS reset to your CSS code: (From here)

/* http://meyerweb.com/eric/tools/css/reset/ 
   v2.0 | 20110126
   License: none (public domain)
*/

html, body, div, span, applet, object, iframe,
h1, h2, h3, h4, h5, h6, p, blockquote, pre,
a, abbr, acronym, address, big, cite, code,
del, dfn, em, img, ins, kbd, q, s, samp,
small, strike, strong, sub, sup, tt, var,
b, u, i, center,
dl, dt, dd, ol, ul, li,
fieldset, form, label, legend,
table, caption, tbody, tfoot, thead, tr, th, td,
article, aside, canvas, details, embed, 
figure, figcaption, footer, header, hgroup, 
menu, nav, output, ruby, section, summary,
time, mark, audio, video {
    margin: 0;
    padding: 0;
    border: 0;
    font-size: 100%;
    font: inherit;
    vertical-align: baseline;
}
/* HTML5 display-role reset for older browsers */
article, aside, details, figcaption, figure, 
footer, header, hgroup, menu, nav, section {
    display: block;
}
body {
    line-height: 1;
}
ol, ul {
    list-style: none;
}
blockquote, q {
    quotes: none;
}
blockquote:before, blockquote:after,
q:before, q:after {
    content: '';
    content: none;
}
table {
    border-collapse: collapse;
    border-spacing: 0;
}

It'll reset the CSS effectively, getting rid of the padding and margins.

This worked for me:

#table {
  border-collapse: collapse;
  border-spacing: 0;
}

For images in td, use this for images:

display: block;

That removes unwanted space for me

Adding to vectran's answer: You also have to set cellspacing attribute on the table element for cross-browser compatibility.

<table cellspacing="0">

EDIT (for the sake of completeness I'm expanding this 5 years later:):

Internet Explorer 6 and Internet Explorer 7 required you to set cellspacing directly as a table attribute, otherwise the spacing wouldn't vanish.

Internet Explorer 8 and later versions and all other versions of popular browsers - Chrome, Firefox, Opera 4+ - support the CSS property border-spacing.

So in order to make a cross-browser table cell spacing reset (supporting IE6 as a dinosaur browser), you can follow the below code sample:

table{
  border: 1px solid black;
}
table td {
  border: 1px solid black; /* Style just to show the table cell boundaries */
}


table.no-spacing {
  border-spacing:0; /* Removes the cell spacing via CSS */
  border-collapse: collapse;  /* Optional - if you don't want to have double border where cells touch */
}

<p>Default table:</p>

<table>
  <tr>
    <td>First cell</td>
    <td>Second cell</td>
  </tr>
</table>

<p>Removed spacing:</p>

<table class="no-spacing" cellspacing="0"> <!-- cellspacing 0 to support IE6 and IE7 -->
  <tr>
    <td>First cell</td>
    <td>Second cell</td>
  </tr>
</table>