Is it OK to tell your password to your company's sysadmin?

Short answer:

ABSOLUTELY NOT!
Your password is between you, and your computer alone.
No one else.

Not your boss, his boss, the system administrator, your bank official, your insurance agent, your ISP support technician, or your cat. Well, your cat you can tell, if she promises not to share it.

There is NEVER a good reason to share a password.
There are many reasons NOT to. Mostly, because a password is YOUR authentication, and as soon as even ONE other person knows it, it can no longer prove your identity.

Any reason your admin comes up with, is bogus, either because he is malicious, lazy, misinformed, or incompetent.
That said, it may not be his fault, but the fault of his organization. Either way, there is incompetence, ignorance and laziness abound.

If an admin, or ANY support technician asks for your password, the correct response is to LAUGH.
Because there's no way they're serious, right?

If your admin insists - explain to him that you will document sharing your password with him... and that, based on this, you are going to send nasty emails to all around - not about him, but you will claim that they came from him (using your account, in your name, using your password that you just shared with him). Of course he won't be able to prove that he didn't misuse your password... which is the point.

No, on second thought, just don't give him your password. It's yours, between you and the computer alone.

Let's try another idea: would you give one of your finger to your IT manager so that he can repair your access to your building while you are working?

I'll assume the answer is no. The same applies to your password. Even if you have a single password for all your services (Which never happens, even for me I confess) the password should NEVER EVER shared with anyone. It's is the only thing that can authenticate yourself. That can bother you having to waste time with your IT support, but this can also send you to jail for a long time.

So, definitely: no

It was explained before that nobody should ever give its password to an administrator (i'm ok with all of it), but you should check with his superior what's going on, because if he asked yours, it's possible that he asked the password of the 18 others ( the 19th is probably his superior) and i'm pretty sure that some of your fellow co-workers use the same password everywhere.