Mine has the ability Oblivious and has amazingly high Attack and Amazingly low Speed. It has no moves besides Zen Headbutt (which is there for Fighting weakness) with base power below 100 most of the time. It knows:
Zen Headbutt: Good power, decent accuracy, decent chance to cause flinching (although that will almost never matter,) used to deal with Fighting types.
Gyro Ball: High power with low Speed. You know the Pokemon has low Speed when Wild Lickitung sometimes hold the Lagging Tail (mine doesn't, it holds the Shell Bell.)
Return: High damage because my Lickilicky is so happy. Also high accuracy and STAB.
Power Whip: Where there's a whip there's a way (sing it). Anybody know what that is from. No? Oh well. This move has high power.