The psychological evidence is quite clear: using a cell phone while you're driving is distracting. Conversing with someone on the phone imposes a cognitive strain that makes it harder for the brain to concentrate on other tasks. Hands-free systems keep drivers eyes on the road, but they don't do much to reduce their level of distraction. No matter how you cut it, the case for banning drivers from using mobile phones is a strong one.
What's less clear is whether or not these bans actually reduce road accidents. Given that mobile technology is fairly new, the question hasn't received much empirical attention. One study to look at texting bans in four states, back in 2010, actually found that accidents increased in those states, compared to neighboring states without the bans — perhaps because drivers tried to hide their phones while texting, making the act even more dangerous.