Using ssh keys for multiple sites

If you have an active ssh-agent that has your id_rsa key loaded, then the problem is likely that ssh is offering that key first. Unfuddle probably accepts it for authentication (e.g. in sshd) but rejects it for authorization to access the company repositories (e.g. in whatever internal software they use for authorization, possibly something akin to Gitolite). Perhaps there is a way to add your personal key to the company account (multiple people are not sharing the same corp_rsa public and private key files, are they?).

The IdentitiesOnly .ssh/config configuration keyword can be used to limit the keys that ssh offers to the remote sshd to just those specified via IdentityFile keywords (i.e. it will refuse to use any additional keys that happen to be loaded into an active ssh-agent).

Try these .ssh/config sections:

Host {personalaccount}.unfuddle.com
     IdentityFile ~/.ssh/id_rsa
     IdentitiesOnly yes

Host {companyaccount}.unfuddle.com
     IdentityFile ~/.ssh/{companyaccount}_rsa
     IdentitiesOnly yes

Then, use Git URLs like these:

git@{personalaccount}.unfuddle.com:{personalaccount}/my-stuff.git
git@{companyaccount}.unfuddle.com:{companyaccount}/their-stuff.git

If you want to take full advantage of the .ssh/config mechanism, you can supply your own custom hostname and change the default user name:

Host uf-mine
     HostName {personalaccount}.unfuddle.com
     User git
     IdentityFile ~/.ssh/id_rsa
     IdentitiesOnly yes

Host uf-comp
     HostName {companyaccount}.unfuddle.com
     User git
     IdentityFile ~/.ssh/{companyaccount}_rsa
     IdentitiesOnly yes

Then, use Git URLs like these:

uf-mine:{personalaccount}/my-stuff.git
uf-comp:{companyaccount}/their-stuff.git

E.g. if I have multiple machines, I'd need to duplicate private keys, which I think is undesirable.

No, actually you don't. If you have multiple machines, you just create a separate private key on each one. For each private key, just upload the corresponding public key to GitHub using the same process.

Also, if my HDD go kaput, I'll lose my private key, which (I guess) is undesirable as well.

Not really; if you lose your private key, just generate a new one and upload the corresponding public key.

For what it's worth, you're right that duplicating a private key is highly undesirable. Ideally, a private key should be generated in one file (~/.ssh/id_rsa for example) and should never leave that file - that is, it should never be copied, moved, and especially not transferred over a network. (e.g. I exclude them from backups) Because of the nature of asymmetric authentication protocols, you only need to worry about keeping your private key out of the hands of others. If you go a bit overboard and you lose track of it yourself, it's generally not a big deal. (This is not to be confused with asymmetric encryption private keys, e.g. GPG keys, which you probably want to hold on to.)