Symptom:
You are trying to install or build Wine from either the official Ubuntu repositories or from the PPA and are constantly receiving dependency errors.
Cause:
Multiarch is supposedly working on Ubuntu now so you should see everything work! You won't.
Solution:
$ sudo dpkg --add-architecture i386
$ sudo apt-get update
$ sudo install wine
$ sudo apt-get update
$ sudo install wine
Apt will now pull the FULL dependency list. The same is true for apt-get build-dep.