With Mac OS 10.7 ("Lion") and above, Macintoshes can no longer run programs written for pre-intel Macs, as was the case in OS 10.5 and 10.6 via the "Rosetta" compatibility layer.
There are some options, though, as detailed below:
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Run a Mac OS 10.5 Virtual Machine on your 10.7+ Mac
It is possible, if you have plenty of spare RAM and disk space, to run a Mac OS 10.5 ("Leopard") virtual machine within your 10.7+ installation. The virtual machine will happily run pre-intel (PPC) code for the forseeable future.
Even better, this virtual machine runs under Sun/Oracle's free "virtualbox" software so there's no outlay to keep your applications running.
There are some tricks to be aware of with regards to the version of virtualbox you run (4.1.8 is the best at the time of writing) and the mode your Mac is running in (32 vs 64-bit). Please see Julian for more information if this system could be of interest to you.
Run a windows version of your app via WINE
If your important application hasn't yet been made compatible with Mac OS 10.7+, but a comparable windows version exists, then it may be worth looking at a system called WINE.
WINE is very clever - your Mac thinks it is running a standard x-windows application, and WINE sends the windows ".exe" executable the kind of signals that it would expect from the windows OS. You do not need to install windows at all, the windows application runs pretty much "natively".
There are lots of flavours of WINE, some commercial (like "crossover"), some are mac-friendly pakaged up and free to use (like "winebottler") or you can compile your own from the open-source original (http://www.winehq.org/)
See Julian if you want to know more
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