I feel like I've posted this all over the internet today, but I thought I'd give the Ubuntu forums a go as well.

Case: wine won't install. At all. The following happens when running sudo apt-get install wine:

The following packages have unmet dependencies:
 wine : Depends: wine1.5 but it is not going to be installed
E: Unable to correct problems, you have held broken packages
Then, trying sudo apt-get install wine1.5:

The following packages have unmet dependencies:
 wine1.5 : Depends: wine1.5-i386 (= 1.5.16-0ubuntu1)
E: Unable to correct problems, you have held broken packages
Then, trying sudo apt-get install wine1.5:i386:

The following packages have unmet dependencies:
 libunity-webapps0 : Depends: unity-webapps-service but it is not going to be installed
 openssh-client : Depends: adduser (>= 3.10) but it is not going to be installed
                  Depends: passwd
 ssh : Depends: openssh-server
 wine1.5:i386 : Depends: wine1.5-i386:i386 (= 1.5.16-0ubuntu1) but it is not going to be installed
                Depends: binfmt-support:i386 (>= 1.1.2)
                Depends: procps:i386
                Recommends: cups-bsd:i386
                Recommends: gnome-exe-thumbnailer:i386 but it is not installable or
                            kde-runtime:i386 but it is not going to be installed
                Recommends: ttf-droid:i386 but it is not installable
                Recommends: ttf-liberation:i386 but it is not installable
                Recommends: ttf-mscorefonts-installer:i386
                Recommends: ttf-umefont:i386 but it is not installable
                Recommends: ttf-unfonts-core:i386 but it is not installable
                Recommends: ttf-wqy-microhei:i386 but it is not installable
                Recommends: winbind:i386
                Recommends: winetricks:i386 but it is not going to be installed
                Recommends: xdg-utils:i386 but it is not installable
E: Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages.
And today, I downloaded Crossover and tried installing the .deb with dpkg. Which gave me this:

Selecting previously unselected package ia32-crossover.
(Reading database ... 186088 files and directories currently installed.)
Unpacking ia32-crossover (from ia32-crossover_11.3.1-1_amd64.deb) ...
dpkg: dependency problems prevent configuration of ia32-crossover:
 ia32-crossover depends on ia32-libs | ia32-apt-get; however:
  Package ia32-libs is not installed.
  Package ia32-apt-get is not installed.
 ia32-crossover depends on lib32gcc1; however:
  Package lib32gcc1 is not installed.
 ia32-crossover depends on lib32nss-mdns; however:
  Package lib32nss-mdns is not installed.
 ia32-crossover depends on lib32z1; however:
  Package lib32z1 is not installed.
 ia32-crossover depends on lib32asound2; however:
  Package lib32asound2 is not installed.

dpkg: error processing ia32-crossover (--install):
 dependency problems - leaving unconfigured
Processing triggers for doc-base ...
Processing 1 added doc-base file...
Registering documents with scrollkeeper...
Errors were encountered while processing:
Then, when running sudo apt-get -f install afterwords:

The following packages were automatically installed and are no longer required:
  bluez-alsa:i386 glib-networking:i386 gstreamer0.10-plugins-base:i386 gstreamer0.10-plugins-good:i386 gstreamer0.10-x:i386 gtk2-engines:i386
  gtk2-engines-murrine:i386 gtk2-engines-oxygen:i386 gtk2-engines-pixbuf:i386 gvfs:i386 gvfs-libs:i386 ibus-gtk:i386 lib32asound2 lib32gcc1
  lib32nss-mdns lib32z1 libaa1:i386 libacl1:i386 libaio1:i386 libao-common libao4:i386 libasn1-8-heimdal:i386 libasound2:i386
  libasound2-plugins:i386 libasyncns0:i386 libatk1.0-0:i386 libattr1:i386 libaudio2:i386 libaudiofile1:i386 libavahi-client3:i386
  libavahi-common-data:i386 libavahi-common3:i386 libavc1394-0:i386 libbz2-1.0:i386 libcaca0:i386 libcairo-gobject2:i386 libcairo2:i386
  libcanberra-gtk-module:i386 libcanberra-gtk0:i386 libcanberra0:i386 libcap2:i386 libcapi20-3:i386 libcdparanoia0:i386 libcomerr2:i386
  libcroco3:i386 libcups2:i386 libcupsimage2:i386 libcurl3:i386 libdatrie1:i386 libdb5.1:i386 libdbus-1-3:i386 libdbus-glib-1-2:i386 libdv4:i386
  libesd0:i386 libexif12:i386 libexpat1:i386 libffi6:i386 libflac8:i386 libfontconfig1:i386 libfreetype6:i386 libgail-common:i386 libgail18:i386
  libgconf-2-4:i386 libgcrypt11:i386 libgd2-xpm:i386 libgdbm3:i386 libgdk-pixbuf2.0-0:i386 libgettextpo0:i386 libglib2.0-0:i386
  libgnome-keyring0:i386 libgnutls26:i386 libgpg-error0:i386 libgphoto2-2:i386 libgphoto2-port0:i386 libgpm2:i386 libgssapi-krb5-2:i386
  libgssapi3-heimdal:i386 libgstreamer-plugins-base0.10-0:i386 libgstreamer0.10-0:i386 libgtk2.0-0:i386 libgudev-1.0-0:i386
  libhcrypto4-heimdal:i386 libheimbase1-heimdal:i386 libheimntlm0-heimdal:i386 libhx509-5-heimdal:i386 libibus-1.0-0:i386 libice6:i386
  libidn11:i386 libiec61883-0:i386 libieee1284-3:i386 libjack-jackd2-0:i386 libjasper1:i386 libjbig0:i386 libjpeg-turbo8:i386 libjpeg8:i386
  libjson0:i386 libk5crypto3:i386 libkeyutils1:i386 libkrb5-26-heimdal:i386 libkrb5-3:i386 libkrb5support0:i386 liblcms1:i386 libldap-2.4-2:i386
  libllvm3.1:i386 libltdl7:i386 liblzma5:i386 libmad0:i386 libmikmod2:i386 libmng1:i386 libmpg123-0:i386 libmysqlclient18:i386 libncurses5:i386
  libncursesw5:i386 libnspr4:i386 libnss3:i386 libodbc1:i386 libogg0:i386 libopenal1:i386 liborc-0.4-0:i386 libp11-kit0:i386 libpango1.0-0:i386
  libpciaccess0:i386 libpcre3:i386 libpixman-1-0:i386 libpng12-0:i386 libproxy1:i386 libpulse-mainloop-glib0:i386 libpulse0:i386 libpulsedsp:i386
  libqt4-dbus:i386 libqt4-declarative:i386 libqt4-designer:i386 libqt4-network:i386 libqt4-qt3support:i386 libqt4-script:i386
  libqt4-scripttools:i386 libqt4-sql:i386 libqt4-sql-mysql:i386 libqt4-svg:i386 libqt4-test:i386 libqt4-xml:i386 libqt4-xmlpatterns:i386
  libqtcore4:i386 libqtgui4:i386 libqtwebkit4:i386 libraw1394-11:i386 libroken18-heimdal:i386 librsvg2-2:i386 librsvg2-common:i386 librtmp0:i386
  libsamplerate0:i386 libsane:i386 libsasl2-2:i386 libsasl2-modules:i386 libsdl-image1.2:i386 libsdl-mixer1.2:i386 libsdl-net1.2:i386
  libsdl-ttf2.0-0:i386 libsdl1.2debian:i386 libselinux1:i386 libshout3:i386 libslang2:i386 libsm6:i386 libsndfile1:i386 libsoup-gnome2.4-1:i386
  libsoup2.4-1:i386 libspeex1:i386 libspeexdsp1:i386 libsqlite3-0:i386 libssl0.9.8:i386 libssl1.0.0:i386 libstdc++5:i386 libstdc++6:i386
  libtag1-vanilla:i386 libtag1c2a:i386 libtasn1-3:i386 libtdb1:i386 libthai0:i386 libtheora0:i386 libtiff5:i386 libtinfo5:i386
  libtxc-dxtn-s2tc0:i386 libudev0:i386 libunistring0:i386 libusb-0.1-4:i386 libusb-1.0-0:i386 libuuid1:i386 libv4l-0:i386 libv4lconvert0:i386
  libvisual-0.4-0:i386 libvorbis0a:i386 libvorbisenc2:i386 libvorbisfile3:i386 libwavpack1:i386 libwebp2:i386 libwind0-heimdal:i386 libwrap0:i386
  libx11-6:i386 libx11-xcb1:i386 libxau6:i386 libxaw7:i386 libxcb-glx0:i386 libxcb-render0:i386 libxcb-shm0:i386 libxcb1:i386 libxcomposite1:i386
  libxcursor1:i386 libxdamage1:i386 libxdmcp6:i386 libxext6:i386 libxfixes3:i386 libxft2:i386 libxi6:i386 libxinerama1:i386 libxml2:i386
  libxmu6:i386 libxp6:i386 libxpm4:i386 libxrandr2:i386 libxrender1:i386 libxslt1.1:i386 libxss1:i386 libxt6:i386 libxtst6:i386 libxv1:i386
  libxxf86vm1:i386 odbcinst odbcinst1debian2 odbcinst1debian2:i386 xaw3dg:i386
Use 'apt-get autoremove' to remove them.
The following extra packages will be installed:
  lib32asound2 lib32gcc1 lib32nss-mdns lib32z1
The following packages will be REMOVED:
  ia32-crossover intel-gpu-tools libdrm-nouveau2 libgl1-mesa-dri libva-x11-1 ubuntu-desktop vlc xorg xserver-xorg-video-ati
  xserver-xorg-video-intel xserver-xorg-video-modesetting xserver-xorg-video-openchrome xserver-xorg-video-radeon xserver-xorg-video-vmware
The following NEW packages will be installed:
  lib32asound2 lib32gcc1 lib32nss-mdns lib32z1
I'm not comfortable with removing 'intel-gpu-tools', 'ubundu-desktop', and all the 'xorg' and 'xserver-*' packages. The same thing happens when booting from a live USB install. But, when installing 12.10 x64 in VirtualBox (the same .iso file as I used to create the live USB) – it works!

I've also asked this question at askubuntu.com.