As of today, perhaps 20
Generally what makes a "core developer" as opposed to a "contributing developer" is an ongoing interest in the codebase that typically equates to near full-time employment. Should all core developers fall under the wheels of this continent-spanning bus of doom then Bitcoin would suffer a significant blow.
For a while.
Then various contributing developers (of which there are legion) would likely step up to act as replacements. The discussions on the forums, IRC channels, mailing lists and version control systems will be read and acted upon. Bugs will be fixed and life will go on.
Edit: So where does this number "20" come from? Well it's based largely on my experiences from reading the development mailing list, IRC logs and various Google+ circles. There is no real exact number, though, activity varies over time and various people are "core" to a particular issue as it passes through.
Are there any known issues that will mean trouble for Bitcoin in the future if there is no future development? i.e could it continue forever without any protocol changes (excluding any undiscovered flaws)? – kirian – 2012-01-31T23:17:44.720
1@kirian - part of what keeps the economy going is that they see a healthy development community. There are various issues to be tackled, features to be added, a massive scaling effort to be designed and implemented. Without core developers, this can't happen. – ripper234 – 2012-02-01T00:17:04.477
1I agree that there is plenty of room for development and improvement but your question just prompted me to wonder if Bitcoin as it currently is could survive indefinitely without any further work. Maybe it should be a separate question on the stackexchange. – kirian – 2012-02-01T00:33:56.447
2@kirian As to whether it could survive without any work, I would say, not really. Technology is changing quite fast nowadays, so at least minor tweaks are needed every now and then. For example, I don't know whether the current client could be installed on Chrome OS, which might become an important system eventually. Moreover, in about 50 years the power of GPUs should be high enough to brute force the current cryptography of Bitcoin and thus make it obsolete (at least if they follow Moore's law). – ThePiachu – 2012-02-01T01:11:22.033