Apart from the above mentioned chmod +x file, another problem might be a missing library. To check the required libraries, use ldd:
$ ldd /bin/sh
linux-vdso.so.1 => (0x00007fffb43fe000)
libc.so.6 => /lib/libc.so.6 (0x00007fc4abe11000)
/lib64/ld-linux-x86-64.so.2 (0x00007fc4ac183000)
If one of these lines shows a missing library, you'll know what needs to be installed before you can run your program.
Another possibility is if your program is a script (shell, perl, python or other text-based program). The first line looks like:
#!/usr/bin/perl
If that file cannot be found, you'll get a permission denied error.