Furthermore, how important is suspension on a bike?
Bicycle suspension is only an important factor when considering the terrain that you will be riding on. You simply don't need it if you don't go offroad. Suspension adds cost and weight to a bike, and it requires additional maintenance—which most people can't do on their own.
Secondly, do road bikes have suspension? If you are speaking of traditional race designed road bikes then no, they do not have suspensions. If you are asking the question of all road bikes then the answer is yes, some newer “endurance” road bikes do have suspensions. This is a high end bicycle that has a rear suspension (see photo below).
Considering this, which suspension is better for bikes?
Now a days, monoshock or single shock absorber at the rear is preferred in most of the bikes because of its better performance and sporty looking characteristics.
Do fat bikes need suspension?
The majority of fat bike riders run rigid forks and claim there's no need for suspension, though this summer fat biker begs to differ. Remember, a suspension fork should smooth out the bumps up front, not the tire, and higher pressure allows you to roll more efficiently.