make sure you set AutoPostBack Property of DropDownList to True in aspx
<asp:dropdownlist id="ddlCompany" runat="server" onselectedindexchanged="ddlCompany_SelectedIndexChanged" autopostback="true" xmlns:asp="#unknown" />
the below is your event handler in code behind
protected void ddlCompany_SelectedIndexChanged(object sender, EventArgs e)
{
string strCompID = ddlCompany.SelectedValue.ToString();
}