How to add a dropdown field in a Gridview?

Create a ItemTemplate in GridView. And Place DropDown inside your ItemTemplate.

If DropDown Items are dynamic add datasource to bind the DropDown.

Use this code I think this will give you complete solution.

<asp:GridView id="grdSystemInfo" runat="server" Width="940px"
                       Font-Names="Verdana" Font-Size="Small" UseAccessibleHeader="False"  PageSize="5"
                       AllowPaging="True" OnPageIndexChanging="grdSystemInfo_PageIndexChanging" onrowcommand="grdSystemInfo_RowCommand"
                       >
           <PagerStyle Font-Bold="True"  />
           <HeaderStyle Font-Names="Verdana" Font-Size="Small" Font-Bold="True" BackColor="#E0E0E0"  />
           <Columns>
           <asp:BoundField DataField="DateTimes"  HeaderText="DateAccessed" />
           <asp:TemplateField HeaderText="Search By">
           <ItemTemplate>
               <asp:DropDownList ID="DropDownList2" runat="server"  OnSelectedIndexChanged="drpl2_selectedIndexChange" AutoPostBack="true">
               <asp:ListItem>Monitor Details</asp:ListItem>
               <asp:ListItem>KeyBoard Details</asp:ListItem>
               <asp:ListItem>Mouse Details</asp:ListItem>
               <asp:ListItem>Processor Details</asp:ListItem>
               <asp:ListItem>O/S Details</asp:ListItem>
               <asp:ListItem>HardDisk Details</asp:ListItem>
               </asp:DropDownList>
           </ItemTemplate>
           </asp:TemplateField>
           </Columns>
       </asp:GridView>

protected void drpl2_selectedIndexChange(object sender, EventArgs e)
{
// get reference to the row
GridViewRow gvr = (GridViewRow)(((Control)sender).NamingContainer);
// Get the reference of this DropDownlist
DropDownList ddlItem = (DropDownList)gvr.FindControl("DropDownList2");
//do the processing here
}