Go to episerver.config file, then find the siteSettings tag and change the uiEditorWidth="500" setting :) 

Thanks for the reply Lars, but it's not the Editor that I want to make wider. It's a textbox for a property under the Information tab.

If you go to Edit Mode, choose a page and go to the Edit tab, then go to the Information tab, you see a list of controls (textboxes, checkboxes, etc) - one for each property. How can I change these controls? e.g. add a new CSS class to a textbox.

If you use a custom property, you can set all your properties like this:

public override void CreateEditControls()
{
    base.CreateEditControls();
    _tb = this.EditControl;
    _numbOfRows = [fetch from config file];
    if(_numbOfRows == -1)
    {
        // Default values if nothing else declared in config file
        _numbOfRows = 4;
    }
    _tb.Columns = 84;   // ***** This is the width property!!  *****
    _tb.TextMode = TextBoxMode.MultiLine;
    _tb.Rows = _numbOfRows;
    _tb.Style["font-family"] = "Arial, Helvetica, Sans-Serif";
    _tb.Text = ToString();
    _tb.ID = Name;

    SetupEditControls();
}

If you want to create a css class, you can select your input tags by using . instead of #.  # is for selecting by ID and . is for selecting by class name. It depends on which order the css files are read (don't remember right now....), but if your custom css file is read last, this should work:
input.episize240
{
width: 200px;
}

Thanks Lars.

In the end we used a '.browser' file to hook up an adapter to render the control differently, as described on this page:

http://sdk.episerver.com/library/cms5/Developers%20Guide/Web%20Controls/Property%20Types.htm

We customised the code a little so that it would only adapt controls with a specific ID, instead of adapting all short string properties.