Everyone seems to like while (true):
https://stackoverflow.com/a/224142/1508519
https://stackoverflow.com/a/1401169/1508519
https://stackoverflow.com/a/1401165/1508519
https://stackoverflow.com/a/1401164/1508519
https://stackoverflow.com/a/1401176/1508519
According to SLaks, they compile identically.
Ben Zotto also says it doesn't matter:
It's not faster.
  If you really care, compile with assembler output for your platform and look to see.
  It doesn't matter. This never matters. Write your infinite loops however you like.
In response to user1216838, here's my attempt to reproduce his results.
Here's my machine:
cat /etc/*-release
CentOS release 6.4 (Final)
gcc version:
Target: x86_64-unknown-linux-gnu
Thread model: posix
gcc version 4.8.2 (GCC)
And test files:
// testing.cpp
#include <iostream>
int main() {
    do { break; } while(1);
}
// testing2.cpp
#include <iostream>
int main() {
    while(1) { break; }
}
// testing3.cpp
#include <iostream>
int main() {
    while(true) { break; }
}
The commands:
gcc -S -o test1.asm testing.cpp
gcc -S -o test2.asm testing2.cpp
gcc -S -o test3.asm testing3.cpp
cmp test1.asm test2.asm
The only difference is the first line, aka the filename.
test1.asm test2.asm differ: byte 16, line 1
Output:
        .file   "testing2.cpp"
        .local  _ZStL8__ioinit
        .comm   _ZStL8__ioinit,1,1
        .text
        .globl  main
        .type   main, @function
main:
.LFB969:
        .cfi_startproc
        pushq   %rbp
        .cfi_def_cfa_offset 16
        .cfi_offset 6, -16
        movq    %rsp, %rbp
        .cfi_def_cfa_register 6
        nop
        movl    $0, %eax
        popq    %rbp
        .cfi_def_cfa 7, 8
        ret
        .cfi_endproc
.LFE969:
        .size   main, .-main
        .type   _Z41__static_initialization_and_destruction_0ii, @function
_Z41__static_initialization_and_destruction_0ii:
.LFB970:
        .cfi_startproc
        pushq   %rbp
        .cfi_def_cfa_offset 16
        .cfi_offset 6, -16
        movq    %rsp, %rbp
        .cfi_def_cfa_register 6
        subq    $16, %rsp
        movl    %edi, -4(%rbp)
        movl    %esi, -8(%rbp)
        cmpl    $1, -4(%rbp)
        jne     .L3
        cmpl    $65535, -8(%rbp)
        jne     .L3
        movl    $_ZStL8__ioinit, %edi
        call    _ZNSt8ios_base4InitC1Ev
        movl    $__dso_handle, %edx
        movl    $_ZStL8__ioinit, %esi
        movl    $_ZNSt8ios_base4InitD1Ev, %edi
        call    __cxa_atexit
.L3:
        leave
        .cfi_def_cfa 7, 8
        ret
        .cfi_endproc
.LFE970:
        .size   _Z41__static_initialization_and_destruction_0ii, .-_Z41__static_initialization_and_destruction_0ii
        .type   _GLOBAL__sub_I_main, @function
_GLOBAL__sub_I_main:
.LFB971:
        .cfi_startproc
        pushq   %rbp
        .cfi_def_cfa_offset 16
        .cfi_offset 6, -16
        movq    %rsp, %rbp
        .cfi_def_cfa_register 6
        movl    $65535, %esi
        movl    $1, %edi
        call    _Z41__static_initialization_and_destruction_0ii
        popq    %rbp
        .cfi_def_cfa 7, 8
        ret
        .cfi_endproc
.LFE971:
        .size   _GLOBAL__sub_I_main, .-_GLOBAL__sub_I_main
        .section        .ctors,"aw",@progbits
        .align 8
        .quad   _GLOBAL__sub_I_main
        .hidden __dso_handle
        .ident  "GCC: (GNU) 4.8.2"
        .section        .note.GNU-stack,"",@progbits
With -O3, the output is considerably smaller of course, but still no difference.