Of course, you could also connect a Bluetooth adapter to both phones (yes they're available for both cell and landline phones) and use a Bluetooth headset, which will automatically switch between phones, depending on which is in range.
That's a nicely geeky solution, but it's also a bit expensive.
For less expensive, just take a 5mm->2.5mm adapter from radioshack, open it up, rewire the second stereo connector to a mic jack (return is common), and you have a uber-geek hand-made computer-headset to phone-headset-jack adapter.

JT Moree wrote:
> Alan Dayley wrote:
>>> phone with bluetooth.)  So, I thought it would be cool to have one
>>> headset for both my computer and my phone.  Maybe an adapter or
>>> something to make the computer one work with the phone.  Anyone heard of
>>> such a thing?  Maybe one can be hacked.  Fun!
> 
> Yes the adapters exist but the cost is about the same as just buying two
> separate headsets last time I checked.  I got the ones that expand and
> contract (Ziplink i think)
> 
> --
> JT Morýe
> PC Xperience, Inc.
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