Delete white space between divs

You get whitespace there because you have whitespace inbetween the divs. Whitespace between inline elements is interpreted as a space.

You have:

<div id="left_side">
    <div id="plan">
        <h1>div 1</h1>
    </div>
</div>
<div id="right_side">
    <div id="news">
        <h1>div 2</h1>
    </div>
</div>

Change for:

<div id="left_side">
    <div id="plan">
        <h1>div 1</h1>
    </div>
</div><div id="right_side">
    <div id="news">
        <h1>div 2</h1>
    </div>
</div>

However, this is a bad way to do what you want to do.

You should float the elements if thats what you want to do.

If you want to retain your coding layout, avoid floats and keep each div on it's own line entirely...

<div id="leftSide">Some content here</div><!-- --><div id="rightSide">Some more content here</div>

Use:

float:left;
clear:none;  

In both div