So the other day, I was able to do this in an Ubuntu natty amd64 chroot for the first time.
# cat > /etc/apt/apt.conf.d/multiarch-me
APT::Architectures { "amd64"; "i386"; };
^D
# cat >> /etc/dpkg/dpkg.cfg
foreign-architecture i386
^D
# apt-get update
# apt-get install flashplugin-installer:i386
Reading package lists... Done
Building dependency tree
Reading state information... Done
[...]
The following NEW packages will be installed:
flashplugin-installer:i386 flashplugin-nonfree:i386 gcc-4.5-base:i386
libatk1.0-0:i386 libavahi-client3:i386 libavahi-common-data:i386
libavahi-common3:i386 libc6:i386 libcairo2:i386 libcomerr2:i386
libcups2:i386 libdatrie1:i386 libdbus-1-3:i386 libdrm2:i386
libegl1-mesa:i386 libexpat1:i386 libfontconfig1:i386 libfreetype6:i386
libgcc1:i386 libgcrypt11:i386 libgdk-pixbuf2.0-0:i386 libgl1-mesa-glx:i386
libglib2.0-0:i386 libgnutls26:i386 libgpg-error0:i386 libgssapi-krb5-2:i386
libgtk2.0-0:i386 libgtk2.0-common libice6:i386 libjasper1:i386
libjpeg62:i386 libk5crypto3:i386 libkeyutils1:i386 libkrb5-3:i386
libkrb5support0:i386 libnspr4:i386 libnspr4-0d:i386 libnss3:i386
libnss3-1d:i386 libpango1.0-0:i386 libpcre3:i386 libpixman-1-0:i386
libpng12-0:i386 libselinux1:i386 libsm6:i386 libsqlite3-0:i386
libstdc++6:i386 libtasn1-3:i386 libthai-data libthai0:i386 libtiff4:i386
libudev0:i386 libuuid1:i386 libx11-6:i386 libx11-data libx11-xcb1:i386
libxau6:i386 libxcb-dri2-0:i386 libxcb-render0:i386 libxcb-shape0:i386
libxcb-shm0:i386 libxcb-xfixes0:i386 libxcb1:i386 libxcomposite1:i386
libxcursor1:i386 libxdamage1:i386 libxdmcp6:i386 libxext6:i386
libxfixes3:i386 libxft2:i386 libxi6:i386 libxinerama1:i386 libxrandr2:i386
libxrender1:i386 libxt6:i386 libxxf86vm1:i386 x11-common zlib1g:i386
0 upgraded, 78 newly installed, 0 to remove and 3 not upgraded.
Need to get 15.1 MB/15.6 MB of archives.
After this operation, 48.9 MB of additional disk space will be used.
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It is a truly heady experience, after so many years of talking about the need to properly support multiarch in Debian and Ubuntu, to see support for cross-installation of packages come to fruition. If you've talked to me any time in the past couple of weeks and noticed it's a little hard to get me to change the subject, well, that's why.
Many who have grown accustomed to Debian and Ubuntu's lack of support for installing i386 packages on amd64 (or vice versa) may wonder what the fuss is about. (Whereas others who are well versed in distributions such as Red Hat and SuSE may laugh and wonder what took us so long...) So maybe a few words of explanation are in order.
If you've ever installed ia32-libs on an amd64 machine anywhere; if you've ever noticed a bug where ia32-libs didn't work right because of wrong system paths, or had to file a request for another library to be added to ia32-libs because it wasn't included in the set of libraries Debian decided to package up in this grotesque, all-in-one 32-bit compatibility bundle; if you've ever decided not to install a 64-bit OS on your perfectly 64-bit-capable hardware because of concern that you wouldn't be able to run $random_32-bit_only_application; multiarch is for you.
If you've gotten stuck maintaining a lib32foo "biarch" package in Debian
due to popular demand, multiarch is definitely for you. 
If you've ever cross-compiled software for a different Debian architecture than the one you were running, multiarch is for you.
If you've ever wanted to run binaries for a different architecture under emulation, and found it awkward to set up the library dependencies, multiarch is for you, too.
Because although the .deb world may be a little late to the party, we're also naturally taking things much further than anyone's done with rpm. Multiarch won't just give you the ability to install 32-bit libs on 64-bit systems; it'll give you the ability to install libs for any known architecture on any system. And a whole lot of pain just falls out of the equation in the process. A cross-compiling environment looks the same as a native-compiling environment. An emulated system looks the same as a native system. We can start to seriously consider cross-grading systems from one architecture to another.
And all this is happening now. The groundwork is there in Ubuntu natty. Wheezy will be the release that brings multiarch to Debian. When dpkg 1.16.0 is uploaded to unstable real soon now, the bootstrapping will begin.
I am immensely grateful to everyone who's helped make multiarch a reality - to Tollef, Matt and others for seeding the vision; Aurelien, Matthias and Arthur for their work to ready the toolchain; David and Michael for the apt implementation; Guillem and Raphael for the dpkg implementation, and Linaro's support to help make this possible; and the many other developers who've helped to refine this design over the years in numerous other BoFs, sessions and mailing list threads.
I'm excited to find out what the Debian community will do with multiarch now that it's upon us. Christian, maybe you should start a pool for how long it will take before all the libraries shipped in ia32-libs have been converted to multiarch and we can drop ia32-libs from the archive?