I fixed it and got it working. I had to make changes to my aspx page and my web.config.
ASPX:
Added this to the top of my page:
<%@ Register Assembly="AjaxControlToolkit" Namespace="AjaxControlToolkit" tagprefix="ajaxToolkit"%>
My control now looks like this:
<asp:TextBox ID="txtOrganization" runat="server" Width ="500px" MaxLength ="250"></asp:TextBox>
<asp:ScriptManager ID="ScriptManager1" runat="server" >
<Services>
<asp:ServiceReference Path="AutoComplete.asmx" />
</Services>
</asp:ScriptManager>
<ajaxToolkit:AutoCompleteExtender runat="server" ID="AutoComplete1"
TargetControlID="txtOrganization"
ServicePath="AutoComplete.asmx" ServiceMethod="GetOrganizationList"
MinimumPrefixLength="1" EnableCaching="true"
FirstRowSelected="true">
</ajaxToolkit:AutoCompleteExtender>
As for my web.config, I added the following:
<configSections>
<sectionGroup name="system.web.extensions" type="System.Web.Configuration.SystemWebExtensionsSectionGroup, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35">
<sectionGroup name="scripting" type="System.Web.Configuration.ScriptingSectionGroup, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35">
<section name="scriptResourceHandler" type="System.Web.Configuration.ScriptingScriptResourceHandlerSection, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" requirePermission="false" allowDefinition="MachineToApplication"/>
<sectionGroup name="webServices" type="System.Web.Configuration.ScriptingWebServicesSectionGroup, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35">
<section name="jsonSerialization" type="System.Web.Configuration.ScriptingJsonSerializationSection, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" requirePermission="false" allowDefinition="Everywhere"/>
<section name="profileService" type="System.Web.Configuration.ScriptingProfileServiceSection, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" requirePermission="false" allowDefinition="MachineToApplication"/>
<section name="authenticationService" type="System.Web.Configuration.ScriptingAuthenticationServiceSection, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" requirePermission="false" allowDefinition="MachineToApplication"/>
</sectionGroup>
</sectionGroup>
</sectionGroup>
</configSections>
<system.web>
<pages>
<controls>
<add tagPrefix="asp" namespace="System.Web.UI" assembly="System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"/>
</controls>
</pages>
<customErrors mode="Off"/>
<compilation debug="true" strict="false" explicit="true">
<assemblies>
<add assembly="System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"/>
<add assembly="System.Web.Extensions.Design, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35"/>
<add assembly="System.Design, Version=2.0.0.0, Culture=neutral, PublicKeyToken=B03F5F7F11D50A3A"/>
<add assembly="System.Windows.Forms, Version=2.0.0.0, Culture=neutral, PublicKeyToken=B77A5C561934E089"/>
</assemblies>
</compilation>
<httpHandlers>
<remove verb="*" path="*.asmx"/>
<add verb="*" path="*.asmx" validate="false" type="System.Web.Script.Services.ScriptHandlerFactory, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"/>
<add verb="*" path="*_AppService.axd" validate="false" type="System.Web.Script.Services.ScriptHandlerFactory, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"/>
<add verb="GET,HEAD" path="ScriptResource.axd" type="System.Web.Handlers.ScriptResourceHandler, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" validate="false"/>
</httpHandlers>
<httpModules>
<add name="ScriptModule" type="System.Web.Handlers.ScriptModule, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"/>
</httpModules>
<sessionState mode="InProc" cookieless="false" timeout="240"/>
<!--
The <authentication> section enables configuration
of the security authentication mode used by
ASP.NET to identify an incoming user.
-->
<authentication mode="Forms"/>
<!--
The <customErrors> section enables configuration
of what to do if/when an unhandled error occurs
during the execution of a request. Specifically,
it enables developers to configure html error pages
to be displayed in place of a error stack trace.
<customErrors mode="RemoteOnly" defaultRedirect="GenericErrorPage.htm">
<error statusCode="403" redirect="NoAccess.htm" />
<error statusCode="404" redirect="FileNotFound.htm" />
</customErrors>
-->
<httpRuntime maxRequestLength="16000" useFullyQualifiedRedirectUrl="true" executionTimeout="180"/>
</system.web>
<system.web.extensions>
<scripting>
<webServices>
<!-- Uncomment this line to customize maxJsonLength and add a custom converter -->
<!--
<jsonSerialization maxJsonLength="500">
<converters>
<add name="ConvertMe" type="Acme.SubAcme.ConvertMeTypeConverter"/>
</converters>
</jsonSerialization>
-->
<!-- Uncomment this line to enable the authentication service. Include requireSSL="true" if appropriate. -->
<!--
<authenticationService enabled="true" requireSSL = "true|false"/>
-->
<!-- Uncomment these lines to enable the profile service. To allow profile properties to be retrieved
and modified in ASP.NET AJAX applications, you need to add each property name to the readAccessProperties and
writeAccessProperties attributes. -->
<!--
<profileService enabled="true"
readAccessProperties="propertyname1,propertyname2"
writeAccessProperties="propertyname1,propertyname2" />
-->
</webServices>
<!--
<scriptResourceHandler enableCompression="true" enableCaching="true" />
-->
</scripting>
</system.web.extensions>
<system.webServer>
<validation validateIntegratedModeConfiguration="false"/>
<modules>
<add name="ScriptModule" preCondition="integratedMode" type="System.Web.Handlers.ScriptModule, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"/>
</modules>
<handlers>
<remove name="WebServiceHandlerFactory-Integrated"/>
<add name="ScriptHandlerFactory" verb="*" path="*.asmx" preCondition="integratedMode" type="System.Web.Script.Services.ScriptHandlerFactory, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"/>
<add name="ScriptHandlerFactoryAppServices" verb="*" path="*_AppService.axd" preCondition="integratedMode" type="System.Web.Script.Services.ScriptHandlerFactory, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"/>
<add name="ScriptResource" preCondition="integratedMode" verb="GET,HEAD" path="ScriptResource.axd" type="System.Web.Handlers.ScriptResourceHandler, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"/>
</handlers>
</system.webServer>
Originally, since I'm using asp.net 2.0, the version numbers of System.Web.Extensions was 1.6.... So I had to change it all to 3.5.0.0.
Also, while searching for a solution, alot of people said I had to put a copy of System.Web.Extensions.dll and System.Web.Extensions.Design.dll into the bin folder. I didn't have to do this, I just merely added a reference to them.