Do agents/publishers ever meet their clients in person?

Sometimes. Depends on a variety of factors. I met my agent twice.

I met up with my agent for lunch when I was in New York for a long weekend. It was fun! We didn't talk too much about the business side of things, but we got the chance to get to know each other better.

If you happen to be in the same place, sure. I've met my agent face to face twice since I signed with her (in 2008), both times at conferences we were both attending. I've never met my editor, but if I'm ever in NY, I imagine she'd be happy to get together.

But it's not necessary to meet face to face to get the job done. Phone and email work just fine. I've had plenty of great phone conversations with both editor and agent.

In the UK I think you're far more likely to meet your agent; I'm not sure if it's because we're so much smaller than America, but most agents would want to meet you before signing you up.

Sure, but it's certainly not necessary. My agent lives twelve hundred miles from me, and there's no reason to travel that far and back just to say something that can be said over the phone or by e-mail.

I think most writers meet their agents sooner or later, but it's not necessary for an agent to meet a writer before offering representation. For one, it's not usually practical. The agent may live in New York or San Francisco and the author could be in Santa Fe or Saginaw.

i met my agent before i signed with him. but as his office is only a couple blocks from my gym, it wasn't much of a trek.

I've met with my agent a couple of times now - we live in the same city. It's been great and she's always open to getting together for lunch. We often do more talking about non-writing stuff than the actual ms related stuff.