Protecting software with license keys?

You are really missing the point of what Open Source means!

Admittedly in this regard my expertise is very limited, but as Crazy Idea Guy, I have some thoughts.
Inputting a serial requires that it write to SOMETHING.
If you only have a single exe, and you want it to remember from one session to the next, AND you want it portable, it's got to write to a separate file.
If you don't want a separate file, then you would need the user to input the serial every time, which would be stored in RAM only for the session.

Lots of installed software will write keys to the registry, and time-stamp themselves based on the install date, but that is problematic in a portable app.

What would work is having an algorithm that works on absolute dates.
It would still be dependent on the computer time.

Here's the theory:
The key generated would use the date and some preset info to create a key for a specific date. It could be as simple as using an MD5 or SHA generator for a text file containing, for example:

"April 10, 2010 skjdnfkjsnaksbskakasbdkajbfdkjabfkjabslhbavdsfkjkfdkgf"

Your app would have embedded in it all the keys for every date you can reasonably expect for the lifetime of the software. For five years, that would be 1826 keys, which may not be an unreasonable amount of code. For 10 years, 3652 keys. The app would then compare the inputted key to this list of keys, determine the start date, and then activate the app if the computer date is withing the span of (the start date + x number of days).

Even if the app stores the inputted key in a separate text file, it would be encrypted and difficult to decrypt.

The advantage of this is that it would be fairly easy to automatically generate the keys, and fairly hard to decrypt them. Also, even if the key is shared, it is only valid for a fixed time period no matter when it is inputted, effectively turning itself off after that time period (which is in your original request)

The disadvantage is that it is not unique to the user, so anyone who has the key can use it for that time period. Also, it can be fooled by changing the system time, but in reality any time-dependent key can have a similar weakness.

You might be able to make it user-specific by generating a separate user key, and require both the time key and the user key to work. You would need your app to be able to regenerate the user key internally for comparison.

Hmm.

P.S. The OP didn't say his software would be open source, just that he'd like the key generator to be free/open.