Error when using Update Panel with gridview...?

Question

You need to put the GridView inside ContentTemplate:

<asp:UpdatePanel ID="UpdatePanel1" runat="server" UpdateMode="Conditional">
    <ContentTemplate>
        <asp:GridView ID="GridView1" CssClass="GridGis"
            runat="server" AutoGenerateColumns="False" PageSize="5"
            OnPageIndexChanging="GridView1_PageIndexChanging" AllowPaging="True">
            <Columns>
                <asp:BoundField DataField="nome" HeaderText="Nome" />
            </Columns>
        </asp:GridView>
    </ContentTemplate>
</asp:UpdatePanel>

EDIT : Here's how I have tested your code:

In the markup I have added one HTML input, it's content will not changed after partial postback.

<%@ Page Language="C#" AutoEventWireup="true" CodeBehind="WebForm1.aspx.cs" Inherits="PostbackTest.WebForm1" %>

<!DOCTYPE html>

<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
</head>
<body>
    <form id="form1" runat="server">
        <div>
            <asp:ScriptManager ID="ScriptManager1" runat="server"></asp:ScriptManager>
            <asp:UpdatePanel ID="upd" runat="server">
                <ContentTemplate>
                    <asp:GridView ID="GridView1" CssClass="GridGis"
                        runat="server" AutoGenerateColumns="False" PageSize="3"
                        OnPageIndexChanging="GridView1_PageIndexChanging" AllowPaging="True">
                        <Columns>
                            <asp:BoundField DataField="nome" HeaderText="Nome" />
                        </Columns>
                    </asp:GridView>
                </ContentTemplate>
            </asp:UpdatePanel>
            <input type="text" id="input" />
        </div>
    </form>
</body>
</html>

In the code I populated the gridview with dummy data on Page_Load. Here's the code:

using System;
using System.Collections.Generic;
using System.Web.UI.WebControls;

namespace PostbackTest
{
    public partial class WebForm1 : System.Web.UI.Page
    {
        protected void Page_Load(object sender, EventArgs e)
        {
            if (!IsPostBack)
            {
                GridView1.DataSource = new List<MyClass>(){new MyClass{ID=1, NOME="ad"},
                   new MyClass{ID=2, NOME="sdf"},
                   new MyClass{ID=3, NOME="fgdf"},
                   new MyClass{ID=4, NOME="fgd"},
                   new MyClass{ID=5, NOME="aghfgd"},
                   new MyClass{ID=6, NOME="jhkj"}};
                GridView1.DataBind();
            }
        }

        protected void GridView1_PageIndexChanging(object sender, GridViewPageEventArgs e)
        {

        }

        private class MyClass
        {
            public int ID { get; set; }
            public string NOME { get; set; }
        }
    }
}