My oldest is only 9, so we haven't taken any friends on vacation with us yet, but I wouldn't mind as she gets older. We have often taken a friend of hers with us, and she has gone with friends on a local day trips with the family, like skiing, Six Flags, the zoo, etc. I don't think it defeats the purpose of a family outings at all. First of all, like someone else said, we get enough togetherness that we just plan trips to have fun together, and don't really feel the need to make it exclusive to our family. Secondly, I find that if my kids have a friend with them, they are happier and it makes the whole outing that much more fun for all of us.
When we invite a child, we pay her way, and that includes tickets, food and maybe a small souvenir. Parents always send money anyway, and sometimes the child will use her own money to buy something. If she really wants to, I won't refuse to let her, but usually, I just put everything on the credit card together.
When our child is invited, we always send money with her to cover food and incidentals. We tell the parents she has money, so that they know, and tell our dd to use her own money. Of course, the other parents never let her pay and she usually comes home with most or all of her money.
As she gets older, if we start inviting kids to join us on more lengthy vacations, I might have to ask them to pay. If it involves an airline flight and expensive park tickets like for Disney, I don't think we could afford to treat a friend to everything and would have to ask with the understanding that the friends family would cover those costs. Hotel and food kind of all gets lumped together in one pot, so I don't think I'd ask them to pay for that. Likewise, if someone wanted to take my dd to Disney, I'd fully expect to pay for her.