Comparing it to the alcolhol prohibition like Matonis does, doesn't make sense because it's not like Bitcoins are the only money available. The only advantage of Bitcoins to normal people is that in some cases it is more convenient and cheaper than using banks. That advantage can easily be taken away by banning money transfers to entities who buy or sell Bitcoins. Banks would probably be very happy to comply and report anyone they suspect of doing it. If the only way to buy and sell them is through Localbitcoin and similar sites, the barrier to entry will be too high for most people.
Money in offshore tax havens is somewhat difficult to deposit, and doesn't need to move very often, yet it still provides a very useful service. Bitcoin's "offshore tax heaven" status simply can't be beat, so at the least that will still continue.
There's also the issue that any ban on Bitcoin will be thought of as a stupid law that bans something that doesn't really hurt anyone (it's just digital internet tokens you can use on gambling sites or to buy internet services, what's the big deal?). As such, people will likely think the law is not fair, and will ignore it, just as they do with file sharing and downloading music/movies. The more laws like these that gets passed, the more everyone will become a criminal, and the less people will think of laws, since they're already breaking them, anyway.
