As I understand it you can run into problems when your versions of libraries or compilers are of older versions than the newer kernel was designed to be compiled with. The kernel itself though ought to be backwards-compatible (but is not 100% guaranteed to be).
I compile my own kernel on Debian and have had no problems, though I am running Sid.
I roughly followed the following with some minor changes*: http://mapopa.blogspot.co.uk/2009/01/compiling-2.html
There may be better guides out there but at least following this one your kernel is installed using dpkg so it is automatically added to grub and it can easily be removed using apt, Synaptic or whatever if you want to.
*(I downloaded https://www.kernel.org/pub/linux/ker...x-3.9.4.tar.xz
Because the above is a tar.xz I issued "tar -Jxvf linux-3.9.4.tar.xz" -- note the upper-case 'J'
I didn't disable Xen
I used "make localmodconfig" before "make menuconfig"
To compile I issued "time fakeroot make-kpkg -j 8 --initrd --append-to-version=-myuser kernel_image kernel_headers" so that I could see how long it took, instruct make to use 8 threads where possible and used my own name for the kernel)