Many do fly private—John Travolta and Harrison Ford actually fly themselves—but there are also people who fly commercial. Jessica Alba and her husband have been seen in coach, with the kids in first class.
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Most large airports, such as Amsterdam, London, Vienna, New York, do have dedicated services for VIP travelers. This is usually why we see so many celebrities traveling as though they directly board the plane and skip the airport altogether. For the most part, they do.
These are things that we have to deal with because we don't have the financial means to fly first class. Those seats are extremely expensive. It turns out though, the seats really are so expensive that a lot of celebs also choose to go the coach/economy route.
Bill Gates has a private jet, a Bombardier BD-700. Warren Buffet *had* one, a Challenger 600, which he sold when he bought Netjets. So one could say Buffet owns hundreds of private jets. I know of one family of billionaires in Italy that doesn't have a private jet amongst them, but they're not household names.
Do famous people go through the same security lines at the airport as everyone else? If they're flying on a commercial flight, then yes. If they're sitting in First Class, there will be “priority” lines/queues. Many truly famous people choose private jets.
Chrissy Teigen just revealed how celebrities avoid public airport terminals. In a Twitter Q&A, she explained that celebs pay for a membership to a private terminal. Celebs still go through security, but then a car takes them directly to the plane.
Saudi Prince Alwaleed bin Talal's Airbus A380 – 502 million USD. The world's most expensive private jet belongs to Prince Alwaleed bin Talal of Saudi Arabia who owns an Airbus A380 with a price tag of over 500 million USD.
Rapper Drake's aircraft is the biggest of the celebrity private jets on our list. In its original form, it would have room for not just his entourage but their extended families too! However, like many celebrities, Drake has customized his jet, sacrificing most of the seating to create luxurious spaces.