Any edge triggered device that processes signals from off-board needs extra care. Most coupling paths are on the printed circuit board, and most of the time, multi-layer boards are much more forgiving. We generally use clock speeds to determine the technology needed. Below 5 MHz, double layer boards work quite well. At speeds above 10 MHz, multi-layer boards are often needed, although one can push this to about 20 MHz with very careful layout and design.
Many designers use double sided boards for cost reasons.
Although we generally prefer multi-layer boards for EMI control, with careful design techniques you can avoid many of the more common problems. All critical signal lines must have ground return running parallel to the signal lines. This includes clock distribution, data buses, and edge triggered clock lines. Long runs, if needed, should also be guarded with a dedicated ground trace on each side of the critical traces. Signal filtering is much more critical than with multilayer boards.