I often have to use computers other than my own while at work, and it would be convenient to fire up pagent with my private key. Is it OK to put my passworded private key in a semi-trusted space?
It depends on the systems that this private key gives access to. If it is only to your systems at home, and it only contains your family pictures, not a big deal. But if it protects a corporate firewall, or banking information, I would not.
The SSH keypairs are used to provide a two-factor authentication. There is something you know (the password) and something you have (the SSH private key). If you no more have the exclusivity of an SSH key, or do not control its use, you are infact removing of of the authentication factor.
I'm a bit crazy, but one of my SSH keys is stored on a fingerprint-protected device. With other security measures around this so that the private key is not left on temporary files, etc.
My point is that your private key may be safe for now. But if a bug is found in SSH key-generation algorithm, or if someone gets a copy and use brute-force to find its password, you increase the cahnces of getting hacked. Again, it depends on what you are protecting with your SSH key.
It shouldn't really be down to paranoia - as your key is effectively 'you' on IT systems (as there is not a 100% guaranteed way to prove the person who typed something was you, this is often considered as close as you can get in general systems) so if you don't protect it someone else could be you to whatever level required.
Do you want to have to defend against technically 'provable' evidence that you committed an act?
Are you happy with knowing that you effectively have no confidentiality?
Protect your private key - always!
From a pure "paranoia with security" perspective, it is NOT ok. Many companies install software on their corporate PCs which are capabale of monitoring everything on those PCs, including keystrokes. (For example, look at this software: Digital Guardian )
In theory, they are able to capture your "password" that is protecting the private key.
In reality, these extreme features (such as key loggers and screen captures) may actually be disabled in most companies.
I am sorry, but whether or not you should have your password protected private key on someone else's PC is a question with subjective answer -- the answer is it depends on your level of paranoia.