Vic, most command line apps, yes. Most need tweaking, and others need only to be told you're using darwin-ppc while compiling. There are also a whole wack of apps that have been ported to run under Darwin so you don't have to fiddle around with any code. Look at these URLs:
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
Running make install as root is only needed if you want to install the software in one of the system directories, so it's available to all users of your system. Most programs will quite happily install into your home directory where you already have all neccessary permissions.
The configuration script is usually calles configure (at least if it was created by autoconf). Every source code should be accompanied by a file called README or INSTALL that details the steps necessary to compile it.
Besides that, if the developers haven't already made the necessary modifictaions for OS X, you will most likely have to make them yourself. There are some hints on how to do this at the pages mentioned by Jadey.