I've read all about this before - the all-important "call." I'd done my homework, researching it on writer's boards, on blogs, on writer websites. I've read what could happen, and what might not happen. I've read about the etiquette, and the details. In fact, here's a GREAT site I referred to the most, pre-call: When Agents Offer Representation. It gives wonderful detail and advice.
My experience happened quickly: the agent offered a contract by email, after reading the full manuscript in 2 days (<--unbelievable!). We spoke on the phone, and I brought up the weather (yes, I know, I can see you rolling your eyes). I was nervous, and wanted to break the ice a little. And, it thankfully worked. He talked about the NY weather, and I mentioned my region, and it flowed into other conversation. That first call, because I was still in contact with other agents, was pretty much only to chat. To hear each other's tone, to see if we could speak on the phone easily, to get our feet wet. It was nice, that I didn't feel I was "selling" myself. He already wanted my book at this point, and made it clear, so I didn't feel pressured to "win him over" on the phone, as I'd imagined it might be.
5 days later, when I'd made my decision to go with his agency, I phoned him at an agreed-upon time, and we hammered out all the details in about 30 minutes -- he talked about an editor who was already interested in my book (yay!!!), and about revisions that would need to be made (thankfully, minor, but when you're talking about a 400-page manuscript, nothing is that minor). We agreed on a general time period for the revisions, and emailed each other with minor questions that same day, back and forth.
In the end, the call wasn't as frightening as I'd feared (well, at least not after that initial two minutes, lol). Mostly, I just reminded myself to breathe, to speak slowly, to let him do much of the talking at first. And yes, I had notes. Questions I wanted to ask, or things I wanted to remember to say. I highly recommend a cheat sheet for that first call, because trust me, your mind could go totally blank and you want to be prepared.
Honestly, I prefer email to phone ('cause I'm a writer, I guess), but that first phone call is CRUCIAL - to hear tone of voice, to see if you "gel" with the agent, to see if your personalities can work together.
To me, looking back, yes, the call was critical/important/necessary. But, in the end, I think it's the combination of things that's even more important to the agent - professionalism from the start (the writer's query letter), quality of the work/novel (which, truly, is what the agent will base his decision on, not the phone call itself), and the willingness of the writer to be flexible and easy to work with.
Oh - one more thing - don't forget that you're also selecting the agent. In other words, this isn't just a one-sided situation. If the agent isn't right for YOU, then listen to your gut and be brave enough to say "no thanks." There's nothing wrong with that. Here's my own example -- there were a couple of agents I'd spoken with about the book who had different "visions" of my book. (In fact, one was willing to offer me representation "if" I'd consider their changes, which were completely drastic). They wanted to change core parts of the book, which would've made it a different book, entirely. I'm not talking about minor plot revisions. I'm really talking more about genre, or even character. It's okay if there are some things you, as the creator of the work, are not willing to change. So, when you're looking for an agent, make sure you have similar visions of the book - that he/she "gets" it. If not, maybe they're not "the one" for you...
Best of luck to those about to receive "the call!" I'd love to hear about your own "call" experiences in the comments, btw...