Our Creator Allah SWT says about the Quran that "this is indeed a Qur'an, most honorable" in Surah Waqiah. This verse makes it clear that Quran is very honorable book and should be respected. Now coming towards the question that is it necessary to do Wudu before touching the Quran.
Well its preferable and better to be in Wudu before touching and reading the Quran but it is not must. nowhere in the Quran or Hadith it is said that Wudu is necessary for touching the Quran. In Islam Wudu is necessary for two things only. one for reading the Salah Prayer and second when you are near Kaaba.
Many of us Muslims respect Quran so much that we keep it on high place in a good cloth and don't do our back towards Quran. We should respect the Quran but what is more important is following the message of Quran. isn't it will be hypocrisy that we give so much respect to Quran but do opposite works to what it teaches us? Read The Quran with translation, then understand it and then follow it.