GetChecked(): boolean

...
function popupControl_Init(s, e) {
    //Synchronize the client variable's value with the confirm dialog checkbox' setting
    dontAskConfirmation = cbDontAsk.GetChecked();
}

function ShowPopup(rowId) {
    //Assign the row's ID value to a specific label within the confirmation dialog, 
    //show the dialog, and set focus to the Yes button
    lbRowId.SetText(rowId);
    popupControl.Show();
    btnYes.Focus();
}

function btnYes_Click(s, e) {
    ClosePopup(true);
}

function btnNo_Click(s, e) {
    ClosePopup(false);
}

function cbDontAsk_CheckedChanged(s, e){
    //Synchronize the client variable's value with the confirm dialog checkbox' 
    //setting, and focus the Yes button
    dontAskConfirmation = cbDontAsk.GetChecked();
    btnYes.Focus();
}
...

...
<dxrp:ASPxRoundPanel ID="ASPxRoundPanel1" runat="server" Width="300px" 
HeaderText="Delete Confirmation" DefaultButton="btnYes">
     <PanelCollection>
         <dxp:PanelContent runat="server">
            <table>
                <tr>
                    <td rowspan="2">
                      <dxe:ASPxImage ID="ASPxImage1" runat="server" ImageUrl="~/Images/img1.png">
                      </dxe:ASPxImage>
                    </td>

                    <td>
                        <dxe:ASPxLabel ID="ASPxLabel1" runat="server" 
                        Text="Are you sure you want to delete this row?">
                        </dxe:ASPxLabel>
                    </td>
                </tr>
                <tr>
                    <td>
                        <dxe:ASPxLabel ID="ASPxLabel2" runat="server" Text="Row ID: " >
                        </dxe:ASPxLabel>    
                        <dxe:ASPxLabel ID="ASPxLabel3" runat="server" 
                        Text="" ClientInstanceName="lbRowId" Font-Bold="True">
                        </dxe:ASPxLabel>     
                    </td>
                </tr>
            </table>
            
 
            <table>
                <tr>
                    <td>
                        <dxe:ASPxCheckBox ID="cbDontAsk" runat="server" 
                        Text="Don't ask confirmation" ClientInstanceName="cbDontAsk">
                            <ClientSideEvents CheckedChanged="cbDontAsk_CheckedChanged" />
                        </dxe:ASPxCheckBox>
                    </td>

                    <td style="width:100%">
                    </td>

                    <td>
                        <dxe:ASPxButton ID="btnYes" runat="server" Text="Yes" Width="50px" 
                             AutoPostBack="False" ClientInstanceName="btnYes">
                            <ClientSideEvents Click="btnYes_Click" />
                        </dxe:ASPxButton>
                    </td>

                    <td>
                        <dxe:ASPxButton ID="btnNo" runat="server" Text="No" 
                             Width="50px" AutoPostBack="False">
                            <ClientSideEvents Click="btnNo_Click" />
                        </dxe:ASPxButton>
                    </td>
                </tr>
            </table>         
         </dxp:PanelContent>
     </PanelCollection>
 </dxrp:ASPxRoundPanel>