If the exchange markets stay open then the price will likely continue to grow, but if they get shut down (which is likely to happen in this world we live in), then the prices will plummet.
They will plummet at least momentarily due to decrease in fungibility, but BTCs will continue to be traded irrespective of whether there are bitcoin exchanges around or not. So, lack of exchanges won't be the end of bitcoin, or necessarily place any fundamental cap on the value of BTC.
Lack of exchanges would make it a lot harder to determine the exchange value of bitcoins against fiat currencies, however.
Joe's Web Shack accepts Bitcoins for hosting services. He wants 3 BTC for a service comparable to $100 USD. Given the current value of the BTC, it's a good deal.
2 days later, exchanges are shutdown and people have very few options of converting BTC into USD. Joe's Web Shack no longer accepts BTC since their value is lost and there's no way to pay the bills with BTCs.
Govt shuts down some BTC exchanges -> BTC value plummets -> Companies accepting them either overprice their goods for BTC or stop taking them -> BTCs are now worthless. It won't be a momentary collapse, it's naive to think so.
