Can I cast a Manic Vandal if there are no artifacts in play?
Manic Vandal says
When Manic Vandal enters the battlefield, destroy target artifact.
You can't cast a spell unless it has legal targets.
When a spell resolves, it will be countered if all of its legal targets are gone.
However, your Manic Vandal spell (the thing that you cast to create Manic Vandal the creature) doesn't actually target. Instead, it just summons a creature. Then, after he enters the battlefield, Manic Vandal's ability -- "When Manic Vandal enters the battlefield, destroy target artifact" -- triggers, and you put the effect "Destroy target artifact" on the stack. If there are no valid targets, nothing is destroyed. But you still get to keep the Manic Vandal creature.
I think it's right to say there are no "targeted creatures" in Magic. Instants/sorceries have targets, and confusingly Auras are cards which are destined to become permanents, but "fizzle" if their target becomes invalid while they're still a spell on the stack. But to date creature spells are exempt from being countered because of lack of legal targets.
Be advised though, that if a creature says something like "when [this] comes into play, destroy target creature", and there are no other creatures in play... no ifs or buts, it has to target and destroy itself!