I am sometimes asked, "If we live in such technologically advanced times, where's my jetpack?" Well, it's being withheld from you on account of you'd either incinerate yourself or crash and die and kill other people along the way, plus it would be crazy bananas expensive. Sorry. Just because it's advanced doesn't mean it ain't stupid.
But because jetpacks have a strong place in our dreamscape (independent flight!), they've always existed in our video games. Jim Rossignol at OffWorld has a nice recap of jetpacks in games through the ages.