Background color of a ListBox item (Windows Forms)

Probably the only way to accomplish that is to draw the items yourself.

Set the DrawMode to OwnerDrawFixed and code something like this on the DrawItem event:

private void listBox_DrawItem(object sender, DrawItemEventArgs e)
{
    e.DrawBackground();
    Graphics g = e.Graphics;

    g.FillRectangle(new SolidBrush(Color.Silver), e.Bounds);

    // Print text

    e.DrawFocusRectangle();
}

The second option would be using a ListView, although they have an other way of implementations (not really data bound, but more flexible in way of columns).

// Set the background to a predefined colour
MyListBox.BackColor = Color.Red;
// OR: Set parts of a color.
MyListBox.BackColor.R = 255;
MyListBox.BackColor.G = 0;
MyListBox.BackColor.B = 0;

If what you mean by setting multiple background colors is setting a different background color for each item, this isn't possible with a ListBox, but it is with a ListView, with something like:

// Set the background of the first item in the list
MyListView.Items[0].BackColor = Color.Red;