Kernel builds with gcc
The recommended compiler for building Linux 2.4 is gcc 2.95. New compilers upto gcc 3.3 have been used successfully to build the kernel however with gcc 3.4 there may be problems when certain configurations. With Linux 2.4 being in deep freeze mode we generally don't intend to fix such problems but rather recommend to use an older compiler for the kernel.
The latest "official" GCC 2 is version 2.95.3. The GCC 2.96 is unofficial massively patched version. It provides more efficient optimization with -O2, more strict syntax checkhing and supports more recent C++ standards. Unfortuntely the C++ ABI is not compatible with "official" 2.95.3 nor 3.0.
Kernels upto 2.6.15 require a gcc 2.95..4.0. Gcc 4.1 is still considered experimental at this point so not recommended where reliability matters. Kernels newer than 2.6.15 require at least gcc 3.2. See a related article on Kerneltrap.
Gcc 3.4.6 incorrectly inlines arch_mem_init().
GCC 4.7.0 and 4.7.1 code generation bug
A bug in these two compiler versions results in bad code for the kernel in such ways that could be taken for a hardware bug, for example error messages about lost interrupts or similar. As of 2012-09-05 the status is that apparently the code generation for __builtin_unreachable() is broken for MIPS and a fix has been checked in upstream but no releases based on that are out yet. It appears that kernels built with -O by modifying the kernel's main makefile are ok. Presumably this is caused by GCC bug 54369.