How to increase scrollbar width in WPF ScrollViewer?

The ScrollBar template reaches out for system parameters to determine its width/height (depending on orientation). Therefore, you can override those parameters:

<ScrollViewer>
    <ScrollViewer.Resources>
        <sys:Double x:Key="{x:Static SystemParameters.VerticalScrollBarWidthKey}">100</sys:Double>
    </ScrollViewer.Resources>
</ScrollViewer>

Here is a XAML solution:

<Style x:Key="{x:Type ScrollBar}" TargetType="{x:Type ScrollBar}">
    <Setter Property="Stylus.IsFlicksEnabled" Value="True" />
    <Style.Triggers>
        <Trigger Property="Orientation" Value="Horizontal">
            <Setter Property="Height" Value="40" />
            <Setter Property="MinHeight" Value="40" />
        </Trigger>
        <Trigger Property="Orientation" Value="Vertical">
            <Setter Property="Width" Value="40" />
            <Setter Property="MinWidth" Value="40" />
        </Trigger>
    </Style.Triggers>
</Style>

And if you don't want to use XAML, you can do it in the Application's constructor, e.g.

using System.Windows;

public partial class App
{
    public App()
    {
        Resources.Add(SystemParameters.VerticalScrollBarWidthKey, 50d);
        Resources.Add(SystemParameters.HorizontalScrollBarHeightKey, 50d);
    }
}

Kent's answer can also be applied to easily all scrollbars in your application by placing it in your App.xaml resources, and by specifying the horizontal height key as well.

<Application
    xmlns:sys="clr-namespace:System;assembly=mscorlib"
    ...
>
    <Application.Resources>
        <sys:Double x:Key="{x:Static SystemParameters.VerticalScrollBarWidthKey}">50</sys:Double>
        <sys:Double x:Key="{x:Static SystemParameters.HorizontalScrollBarHeightKey}">50</sys:Double>
    </Application.Resources>
</Application>