Very light swirls may be removed by hand however it is VERY time consuming and it comes with a lot of elbow grease.
Meguiars Scratch X is a fantastic product. Its formulated to be used by hand however its really meant for quick spot fixes rather than being applied to the entire vehicle. Its not a wipe on/wipe off product. You have to work it in with passion and it may take a few applications.
If you really want to rid the paint effectively and quickly from the unsightly marring then a professional machine would be required. The detailers choice is the
Porter Cable 7424. Its a oscillating polisher that has various speeds. Combined with the right product for the job (and the right TECHNIQUE), it can make a paint finish look flawless.
If your serious about a prestine finish then you should read up and learn on how to use the machine and what products to use for your situation. There are many different polishes out there, each with different levels of abrasives.
Just a few good resources...
www.paintcare-n-detailing.com
www.autopia.org/forum
www.meguiarsonline.com