Yes, Adults should vote
No, it is not important for adults to vote
Maybe if your literally the only person who doesnt vote but when thousands of people have that same mentality, than it can have an affect on the elections.
If a population is not willing to be active in politics then they don't deserve a democracy, they deserve Authoritarianism (not that it's a bad thing)
Local elections are pretty important - speed bumps, traffic lights, property taxes, zoning, etc.
Firstly, this is assuming a democratic system. IMO a democratic system is not necessarily ideal. It may work in some places, and not work in others. Secondly, even in a democratic system, I don't think it's always important to vote. If there are no good candidates whom you truly support, there's no point in voting. If you don't think voting will really bring about a change you want, there's no want in voting. IMO, the idea that voting is a civil responsibility is rather dogmatic, and I'm yet to see good reasons to support that.
No, in fact most people should refrain
What would make a more powerful statement as a nation: Everyone voting because they feel like they HAVE to, or nobody voting at all? Could you imagine the chaos that would ensue if the presidential election ended with 1 vote for each candidate...just them voting for themselves?
Can really only comment about the US, where I live. It really only matters if you live in particular states. Even then one could argue the value in it.