In reply to Double Knee Bar:
I use a mat or towel to ease comfort on a had floor but not to support the back.
You should keep your tummy dished and not create an arch in your back. This is true of other exercises like leg raises etc. If you cannot get your back on the floor you need to amend the exercise to your level of strength/flexibility to protect your back.
To be honest though, i don't really like situps for this reason and prefer crunches or other variations on situps.
Ones where you never completely go flat back on to the ground, and maintain a dish shape instead. Its a harder workout as you are maintaining core stability and balance throughout and you can vary the difficulty of it to protect your back.