In reply to the original question, bitcoins will have value as long as people are willing to trade goods and services for bitcoins. Currently there are some currency exchanges where you can measure bitcoins value against the dollar. So that now 1000BTC is roughly $250. But you shouldn't think only in terms of exchange rate but in terms of goods.
1000BTC now will buy you, what 9 vibrating dildos at the bitcoinsextoys.com (sorry, just found this). These are just goods, goods and services, and as long as people are accepting them then they are worth something.
As for bitcoin being banned, I think that we will have an early trial by fire as it begins to be used in China. This is a totalitarian regime, all currencies are banned except those specifically allowed (Reminbi, or peoples money, also called the Yuan). All activity here involving bitcoin it illegal; therefor bitcoin and it's markets must develope entirely in the black market.
But despite the government power here many people (especially in tourist areas) accept US$ and I think China was the first place to begin accepting digital money as a form of acceptable currency (QQCoin) until the government banned it(bear in mind that QQCoin was not created to be used as a general currency, nor was it encouraged, but it happened anyway).
I do not know how it will exactly begin here but every step it takes is illegal, and therefor must be survivable.