Update 2018: How many Software Developers does it take to change a Lightbulb??? Who Cares!? That's a Hardware Problem!
Generally NO, You don't need to know computer architecture to be a good programmer, That's more in the EE realm IMO.. unless of course you're in embedded systems development, but in that case you're married to the chip and programming right on it, so you'll need to know the architecture of THAT "computer" (and even then it may not matter), but having a general architectural understanding of how computers work wont be good for much else than Water-hole discussions.
I would say it's even less important these days at the rate hardware is declining in price and performance is improving / increasing and how quickly the technologies are changing and languages are evolving. Data structures and design patterns don't really have much to do with physical hardware architecture as far as I know.
Generally Programmers come from a computer science background, in which case, they've more than likely taken computer architecture classes, but now-a-days, Operating Systems are going virtual, disk space is shared, memory is scaleable, etc.. etc..
I have been able to make a great career in programming(10+ years) and I have very little educational knowledge of computer architecture, mostly because... I was an Art major!!!
Update: Just to be fair, MY "little educational knowledge" came from my CPU Sci. Minor. and still, I've never needed to use anything I've learned from my Assembly classes or my Computer Architecture classes in my "Programming" career.
Even now as I play around with some Mesh Networking Idea's implementing the ZigBee spec, I've found that using the products and tools available (XBee), I'm able to program in Python and plop the code right on chip (SoC) and do some really neat stuff with it.. ALL without having to worry about anything to do with actual architecture of the chips, etc.. there are definitely hardware limitations to be cognitive of because of the chip size and the intended low price target.. but even THAT will become less in the upcoming years. So I stand by my "Generally NO" answer