Can creatures abilities target that creature itself?
Can Spikeshot Goblin have itself as a target with its ability: "Tap: Spikeshot Goblin deals damage equal to its power to target creature or player"?


Yes. Spikeshot Goblin is a creature, and unless it somehow gains protection from red, shroud, etc. it's a valid target for its own ability.


  114.5. A spell or ability on the stack is an illegal target for itself.


This only means the ability can't target itself, i.e. the ability itself. This is only relevant in rare cases; one example (for spells) would be that you can't change the target of a Counterspell on the stack to itself. (If you want to counter a Counterspell with e.g. Misdirection, you have to retarget Counterspell to Misdirection; when Counterspell tries to resolve, it will then fizzle because the Misdirection is no longer a valid target, and the original target of Counterspell will not be countered.)