Ahhhh, jet lag. Always "fun" to deal with. Even more "fun" to deal with when you're dealing with your own and that of two small children.
Small time differences (1 to 3 hours)
Since most of our travel has been within the Americas (lower 48 states, Canada, Mexico, Panama, etc.), we're generally dealing with small time differences of 1-3 hours. These aren't too bad.
Back when we lived in California, during Littles' first year, we traveled frequently to Texas (2 hours ahead) and the East Coast (3 hours ahead). We found it was actually good to keep her on roughly the same schedule, i.e. if we started her bedtime routine at 7 PM in California, we started it at 10 PM on the East Coast. Since we were often visiting friends and family, it was nice to be able to, say, go out to dinner at a normal hour and not deal with a cranky, overtired baby. But I don't know how well this strategy would work with an older child, who might naturally start to adjust to the new time.
Now that we live in Texas, we're usually dealing with 1-2 hour shifts. When we travel west, we expect a few mornings of early wake-ups, but the kids usually adjust completely within 2-3 days. When we travel east, we hardly notice a difference.
Medium time difference (6 hours)
We took Littles to England a few months after her second birthday. It's six hours ahead of Texas.
When we arrived, we had a few mornings of really struggling to get her out of bed. Luckily, we were there for a wedding, so we had good motivation to get her up at a reasonable hour, and then there was plenty of activity to keep her up until it was time to sleep again. We were in England for a full week, and while she did tend to sleep a little later than she does back home (waking up between 8-9 AM, rather than 7-8 AM) for the entire time we were there, that still allowed us time to do lots of stuff during the day.
When we returned home, she woke up earlier than usual (about 6 AM) for a full week, but eventually adjusted back to her normal schedule.
Large time difference (14 hours)
China is a full 14 hours ahead of Texas, so jet lag was a big issue on this trip!
We arrived at around dinnertime on Sunday night. The kids had not slept very much on the plane, and conked out pretty quickly that night, so we figured they'd sleep well and be on their way towards adjusting. Wrong! They were both up in the wee hours of the morning on Monday. Then they crashed at around 11 AM, and slept till after 9 PM! (They were just hanging out at the hotel with their Grannie while my husband and I worked, so it was fine for them to sleep most of the day away.)
After that day, we started enforcing a more normal nap/nighttime schedule, waking them up when they slept too long. Still, Noob in particular continued the wee-hours wakeup for a good week after arriving. I was usually the one up with him, and I let him play quietly but kept the room dark. He usually got bored after an hour or so and curled up with me to sleep some more. Both kids also woke up a tad on the early side (around 6 AM) for the first week. By the second week, they were back on a fairly normal schedule.
When we arrived back home, we had originally planned to keep the kids out of school for a day or two to adjust. (Especially Noob, who was starting at preschool for the first time.) But then we figured that school was actually the best place for them to get back on track schedule-wise! So we arrived back home on Tuesday afternoon and they were both in school on Wednesday morning. We warned their teachers that fatigue might lead to cranky/bad behavior, but both kids did well with it. Sleep-wise, Noob adjusted back to a pretty normal schedule within a few days, as did I. Littles woke up earlier than usual for over a week, but my husband was doing the same and so he usually got up with her and they hung out. Within two weeks, both kids were fully adjusted.