People often recommend contributing to open source projects as a good way to learn and to build your resume and reputation. In that case you're not necessarily motivated by an existing product need.
I agree with jrockway (but perhaps not the phrasing) that its not an appropriate response to the requirement.
People advise new programmers, "Its good to have work on an open source project on your resume." because that gives them access to your check-ins, how you responded to reviews, and generally mailing list chatter. That is invaluable for potential managers since its like having a 'preview' of how you work. However ...
When people hear it "Go contribute to some open source project." That is not the correct interpretation. And the reason is that there two conflicting assumptions.
The manager person is looking for folks who write code, whether or not it pays the bills. These are people who love to code. So if you're not already writing code, then your already not someone they really want to talk to.
If you're writing tons of code in your spare time, but none of it is 'out there', then one of three things might be true;
1) You're one of those people for whom someone elses code is never good enough so you've written everything yourself from scratch, probably have your own mail program, dns server, tcp stack, you name it :-)
2) You are keeping all your code under wraps because someday you're going to sell it as the next version of Office or something for $1000/copy. :-)
3) You can't tell if anyone would even care to use your code even if it was available so you just work on it in isolation.
Of these types, if you're #3 the solution is easy, pick a couple of things you're doing, throw them up on github so that there is a copy 'out there' if you need to recover it and you will find people will discover it and start feeding you back comments.
If you're #2 you probably aren't going to be a good fit but feel free to create the next Microsoft. Some of the people in #2 will create the next SAP or Salesforce.com or Autocad so don't let me stop you.
If you're in group #1 you're possibly a brilliant coder who will argue with everyone :-).
When people come to me and ask "How can I get a job at Google?" I ask them what software they are working on. If they answer, "What do you mean?" I explain the whole "If you are someone Google might hire, then you are someone that writes code whether or not you are getting paid for it. If you aren't that type of person then working for Google is probably not high on the list of possibilities (although I hear that is changing).
Shipping a product (even if it's just a dumb little side project) is way more impressive to most people than contributing a patch to an open source project.
I contribute to projects that I use as often as I can, but I've never had to point a potential client to my Github account to land a contract.
Impressive to the average person, yes, but not impressive to people hiring someone to work on a team. It's great to be able to do whatever you want, but it takes a special kind of person to put their personal tastes aside, open up someone else's work, and fix it. Incidentally, that's what most programming jobs are, and most people are terrible at it.
