I'm in the fortunate position that my in laws live close by - so if we ever have a trip planned that isn't pet-friendly we ask them to care for our cat and dog. They are animal lovers too, and have their own dog that gets along very well with our pets also, so it's also a good opportunity for all the pets to socialize together.
I honestly don't know that I could take a vacation somewhere if I didn't know the people caring for my animals. To me, they are such a part of the family that I need to keep them with someone I trust 100%. I guess they're just like our kids, honestly. If we are traveling within the country, rather than overseas, we try to find accommodations that are pet friendly. There are quite a few out there, and even if they don't advertise it we always still ask the question of whether it's possible. Our ideal scenario is being able to keep the pets with us at all times, even on vacations, because truly it feels like a part of our family is missing when they're not around.
Other people I know sometimes board their pets when they go on vacations, I don't see a problem with that as long as the place is a reputable one. I would want personal recommendations from family or friends if I ever had to go down that route, but hopefully I'll always be in a situation where I have a trusted family member or friend nearby who is happy to watch the pets if I simply can't take them with us.