i am sure this has been discussed many times in many different threads. but anyway, the long and shortof it is ...
yes. if you have the source code, and, as Jadey said, if it is a CLI application, you can compile it for OS X and run it
if you don't have the source code, you probably cannot. this is because most precompiled binaries for Linux are for the x86 (processors like the Intel Pentium) architecture.
even if you have compiled Linux binary for PowerPC, it is unlikely that it will run on OS X, because the Linux (YellowDog, LinuxPPC or MkLinux) executable file format is different from OS X
if, however, you have a compiled Darwin binary (this is the core Unix part or OS X), you will have no problem running it under OS X
assuming it is for the right platform, if it is a GUI application. it will probably be for X Windows, not for Aqua. In that case, you will have to have X on your machine - there are various ports of xfree86 and other X-win environments for MacOS X