I've heard differing opinions about this from scholars, and personally I feel like it's okay to pick up the Qur'an without Wudu. (Although, if you can it's obviously encouraged) The verse from the Qur'an that most people point to when discussing this issue is verse 79 from the 56th Surah, Al Waqiah:
That this is indeed a Qur'an most honourable, (77) In a Book well-guarded, (78) Which none shall touch but those who are clean (pure): (79) A Revelation from the Lord of the Worlds. (80)
And my understanding is that this is not referring to purity gained by performing Wudu, but rather the purity of the Angels who handled the Qur'an as it was being revealed. This understanding of the verse makes sense to me, since if you think about it, the Qur'an wasn't a physical book when it was first revealed, but rather a recitation that was memorized. Having Wudu as a mandatory requirement also doesn't make sense in the context of sharing or spreading the message of Islam, since we can't exactly force every non Muslim to make Wudu before they pick up the Qur'an, and if we did it would probably turn most of them away.

I know there are numerous videos on Youtube as well which cover this topic... One by Zakir Naik comes to mind, but I'm sure there are more. I would supply you with links, but seeing as I'm still a limited member, I can't... Sorry!