Are there certain motherboards you need for overclocking CPU?

Solution
You need the Z boards for overclocking with Intel K and X processors which are unlocked. Like z170 for skylake or z97 prior to that.

For AMD, most motherboards are OC ready with the Black Edition chips.
For FM2+ cpus, APUs with k are unlocked.
For AM3+, all are overclockable.
You need the Z boards for overclocking with Intel K and X processors which are unlocked. Like z170 for skylake or z97 prior to that.

For AMD, most motherboards are OC ready with the Black Edition chips.
For FM2+ cpus, APUs with k are unlocked.
For AM3+, all are overclockable.
 
Solution
Yes but depends on processor. For AMD platform it's enough to have a processor with unlocked multiplier of which all FX are and most APU and Athlon processors for FM2/2+ socket.
For Intel processors of newer generation, processor has to have "K" at the designation (unlocked multiplier) and MB that can make use of it, mostly starting with "Z" in their names.
Other requirements would be good VRM (Voltage Regulation Module) that can take increased power load. Good cooling is required in all cases and that usually means aftermarket CPU cooler as well as case ventilation.