They had a working jetpack for a James Bond movie decades ago. There have been slight improvements in flight time/range since but we've hit the point where giving them enough fuel to make the range useful makes them too heavy to work. We need a pretty major breakthrough to solve this issue.

Even then it wouldn't solve the biggest issue which /u/the__storm also pointed out: If the engine fails you are dead or at least seriously injured. Planes and helicopters both have means of performing a non-powered landing, jetpacks wouldn't. No insurance company would cover them. I suppose a heavy-duty parachute would be a potential solution but then you're adding more weight and it wouldn't be a guaranteed safe landing since parachutes need you to be at a certain height so they have time to deploy and slow you down.

Should also touch on the logistical nightmare which would be involved. A jetpack would essentially be a personal aircraft so you would have to submit a flight plan, be aware of and avoid restricted air-space, etc.