Get the compiler options from a compiled executable?

gcc has a -frecord-gcc-switches option for that:

   -frecord-gcc-switches
       This switch causes the command line that was used to invoke the compiler to
       be recorded into the object file that is being created.  This switch is only
       implemented on some targets and the exact format of the recording is target
       and binary file format dependent, but it usually takes the form of a section
       containing ASCII text.

Afterwards, the ELF executables will contain .GCC.command.line section with that information.

$ gcc -O2 -frecord-gcc-switches a.c
$ readelf -p .GCC.command.line a.out 

String dump of section '.GCC.command.line':
  [     0]  a.c
  [     4]  -mtune=generic
  [    13]  -march=x86-64
  [    21]  -O2
  [    25]  -frecord-gcc-switches

Of course, it won't work for executables compiled without that option.

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For the simple case of optimizations, you could try using a debugger if the file was compiled with debug info. If you step through it a little, you may notice that some variables were 'optimized out'. That suggests that optimization took place.

Another option is -grecord-gcc-swtiches (note, not -f but -g). According to gcc docs it'll put flags into dwarf debug info. And looks like it's enabled by default since gcc 4.8.

I've found dwarfdump program to be useful to extract those cflags. Note, strings program does not see them. Looks like dwarf info is compressed.

If you compile with the -frecord-gcc-switches flag, then the command line compiler options will be written in the binary in the note section. See also the docs.