Bitcoin makes _two_ fundamental security assumptions, one of them people talk about all the time: that conspiring badguys don't get control of a near-majority hashpower; the other is that "information [is] easy to spread but hard to stifle": If nodes can't communicate without partitioning they can't come to a consensus, or any consensus they think they have may be false and erased once communication is restored. So in one sense Bitcoin is potentially very vulnerable to censorship.
But at the same time: Bitcoin works great without using the public internet at all— at least if you're using the reference software. There is a whole network of hidden service Bitcoin nodes that communicate over tor without using exits. Connecting out to this network is as simple as installing Tor and pointing Bitcoind / Bitcoin-qt's proxy settings at it.
Receiving connections in on
takes a couple more lines of configuration and is a good idea to do because we can only support a lot of hidden service using nodes if there are a lot of hidden service offering nodes.
Tor has been at the anti-censorship game for a while now and has a fair amount of resources to throw at it and there are some benefits to sharing a network with other kinds of usage... I don't think there is any real concern with censorship in most of the world, but I like my backup plans to have backup plans, and so it's good that there is a health hidden service infrastructure in advance of needing one.
Since I also like the backups of my backups to have backups: More fundamentally, the blockchain validity rules limit the maximum long term average data rate of Bitcoin to only about 14kbit/sec. Because of this low rate there are lot of steganographic techniques that could be employed to keep hosts connected very surreptitiously ("blockchain over cat pictures"), at least if the user isn't mining and can tolerate fairly high latency (Mining is much more sensitive, however, and to keep latency down needs bandwidth a large multiple of the average rate). Beyond steganography over the internet, the low rate means that we could not-unreasonably broadcast Bitcoin data world wide over relatively inexpensive satellite channels or HF or even VLF radio (well, at least headers over VLF). Perhaps a hardfork changes the block size limits in the future, but at least for now in a censorship war I think Bitcoin would fair very well.
So, even though breaking the flow of information breaks Bitcoin fundamentally, our narrow requirements for information and the nature of our communication (broadcats) means that to block Bitcoin, given a community of adaptive users and developers, probably requires blocking damn near everything.
I don't consider censorship a critical risk given our current network parameters, but it's something we could be preparing a little better for, especially making sure that big "hash colocation points" and mining pools aren't big censorship targets that are too conspicuous to vanish.