Consider SomeStringVar as the string you are working with innertext data.

Note I removed the node dashes from your data provided.

Using XDocument.Parse method you can query the data as shown.

Code:
Private Sub Button2_Click( _
   ByVal sender As System.Object, _
   ByVal e As System.EventArgs) _
   Handles Button2.Click

   Dim SomeStringVar As String = _
      <response>
         <result>
            <application_owner>mdcpinpoint</application_owner>
            <application_list>
               <applications>
                  <application>
                     <application_name>Activity Log</application_name>
                     <link_name>activity-log</link_name>
                     <access>private</access>
                     <created_time>2011-12-01 07:33:35.0</created_time>
                  </application>
                  <application>
                     <application_name>Contact</application_name>
                     <link_name>contact</link_name>
                     <access>private</access>
                     <created_time>2011-12-01 07:32:53.0</created_time>
                  </application>
                  <application>
                     <application_name>Visicode New Business</application_name>
                     <link_name>visicode-new-business</link_name>
                     <access>private</access>
                     <created_time>2011-11-24 03:54:19.0</created_time>
                  </application>
               </applications>
            </application_list>
         </result>
      </response>.ToString

   Dim Doc As New XDocument
   Doc = XDocument.Parse(SomeStringVar)

   Dim Test = (From T In Doc...<application> _
               Select Name = T.<application_name>.Value, _
                      Created = T.<created_time>.Value).ToList

   For Each app In Test
      Console.WriteLine("{0} {1}", app.Created, app.Name)
   Next

End Sub
By creating a Schema you can get context help (Intellisense) when writing a LINQ statement

Code:
<?xml version="1.0" encoding="utf-8"?>
<xs:schema 
   attributeFormDefault="unqualified" 
   elementFormDefault="qualified" 
   xmlns:xs="http://www.w3.org/2001/XMLSchema">
  <xs:element name="response">
    <xs:complexType>
      <xs:sequence>
        <xs:element name="result">
          <xs:complexType>
            <xs:sequence>
              <xs:element name="application_owner" type="xs:string" />
              <xs:element name="application_list">
                <xs:complexType>
                  <xs:sequence>
                    <xs:element name="applications">
                      <xs:complexType>
                        <xs:sequence>
                          <xs:element maxOccurs="unbounded" name="application">
                            <xs:complexType>
                              <xs:sequence>
                                <xs:element name="application_name" type="xs:string" />
                                <xs:element name="link_name" type="xs:string" />
                                <xs:element name="access" type="xs:string" />
                                <xs:element name="created_time" type="xs:string" />
                              </xs:sequence>
                            </xs:complexType>
                          </xs:element>
                        </xs:sequence>
                      </xs:complexType>
                    </xs:element>
                  </xs:sequence>
                </xs:complexType>
              </xs:element>
            </xs:sequence>
          </xs:complexType>
        </xs:element>
      </xs:sequence>
    </xs:complexType>
  </xs:element>
</xs:schema>