Running 32 binaries on 64 platform

I have upgraded my hardware to 64 bit processors, and found that some
applications don't have binaries to run on it, such as RealPlayer, or a Java
plugin, or even the latest release of OpenOffice, which did not come with a
distribution. In fact some things I could not even compile from the sources
because they ask for libraries which I don't have, and it's just a pain going
for all the missing packages.

I suspect there should be a way to run 32 binaries on 64 platform in emulation.
I tried to search the web but did not find a direct answer. An advise
is appreciated.

Best regards,

--
Andrei V. Smirnov
MulPhys.com
http://smirnov.mae.wvu.edu