Do you need to be skilled at office politics to succeed in your career?

You need to have a certain amount of people skills, and that includes networking with others. Being able to work with other people, make genuine connections with your team, and having a willingness to learn ALL THE TIME make the biggest impact on how well you succeed.

Not really. I work at the company I do in order to avoid office politics, although if I were interested in a management position I'd still have to put some effort into it.

Of course you do! Everyone does!

Absolutely. Knowing who to go for what (and what not) is crucial to establishing the relationships that either going to get you ahead or set you back.

Yes and no... depends on what type of office politics. You need to understand the culture of the office and want to succeed. You need to "read the room" well and know how you need to fit in.

No, you need to be good at your job.