Most bands these days often do more "hubbing" than flying from city to city. Then again, it also all depends.
Just a few examples, for the fun of it.
On John Mellencamp's tour in 1999, for the midwest amphitheater cities in the summer and during the fall midwest/college cities tour, he and his band would fly in every early night from Bloomington, Indiana and then back again that night. I am not sure of the exact plane it was used, but it had to at least hold up to 15 people.
For the Fleetwood Mac tour of 2003 and 2004 they used a 727 for the entire band and some support crew, assistants. They would 'hub' out of cities (ex. Chicago, L.A., New York, Atlanta), etc. because Mick Fleetwood & Lindsay Buckingham & other musicians with them and crew members had young babies. So they'd move their families into these cities and get a hotel suite, fly out 1-1.5 hours to their performance city, do a show, and go back to their "hub" then move to a different base every month. They'd usually do one night off between shows, too. However in 2004 in the summer they basically did go from one show to the next and didn't do the hub thing since that tour leg was much shorter. In Australia they used a 737.
Jimmy Buffett does the same thing. He does 2 week tour legs then takes a month off then does another leg and usually bases himself out of either NYC, Chicago, L.A., for example and Learjets in with his band members.
Stevie Nicks solo has used a private 727 or a Learjet for all of her tours except for 1998.
Cher used a private jet during the winter 2000 leg of her "Believe" tour, otherwise she goes by bus.
Rather than go exclusively, Tina Turner rode with her entire band and backing dancers on a larger jet in 2000. Bette Midler did the same on her 1999, 2003, and 2004 tours.
On Madonna's tour in 2001 and 2004, she and her family traveled privately on their own Learjet, while the band and dancers traveled by larger leased jet.
Some artists still do use buses from time to time. But when they stay behind or need to go ahead of the tour for whatever the reason, it is not uncommon for them to charter a private Learjet. Some have gone the commercial flying route, but sometimes cancellations of course have led to disasterous consequences. Of course flying solo doesn't always do the best justice, either... at a Madonna show, one of her Washington D.C. performances was delayed by 90 minutes because her private plane was delayed by air traffic.
if assumptions could fly, airliners.net would be the world's busiest airport