Most companies pay a lot of attention to placing members on their boards. On nonprofit boards, members are generally expected to bring their own cash, fundraising contacts, and/or expertise, and they are generally unpaid. For profit companies are usually looking for relevant expertise, contacts, or a prestigious (at least in their field) name. And, as was pointed out before, being on a board brings potential liability. Who pays for the liability insurance is significant.
If you're a retired CEO, 4 Star General, or major stockholder, you will probably get a lot of approaches to be on boards, paid and unpaid. For most of the rest of us, paid board opportunities are very rare. If you dedicate a lot of time and effort to a local nonprofit, you might well be invited to be on the board, but the chances are it will be unpaid.