How important is it to meet photographer

Very VERY important. This is the one vendor that will be, literally, by your side for almost the entire day. You need to know you have common ideas, thoughts, and plans and that you actually get along.

It's extremely important. Out of all the vendors, they're gonna be the ones spending the whooole day with you. I met with two. One of the photographers had beautiful work, and I was excited to meet with him. But when we met in person, I found that the rest of his work wasn't really my style, and he came off as pretty arrogant and pushy to me.
I absolutely love the photographer I picked (the second one I met with). She's so down to earth, her work is gorgeous, and we instantly clicked.

It's very important. Most photographers include an e-shoot in their packages so you can meet them in-person prior to your wedding.

Agreed that it's important.

Can you maybe Facetime or Skype with this woman beforehand to get a feel for her and make sure you click?

Very important. If you can't meet in person at the least you need to do skype or facetime. But in person allows you to get a sense for their personality and they may be able to show you actual photos and books that they have created besides what you see online. Especially if you already have an issue with comfortability. I met two photographers in person and one i did not like he was so short with his discussion and didn't seem to have it all together. Over email i would have had no clue. We were able to discuss the proposed timeline of the day and vision and the type of photos we would like to have and he decided if he thought he was a good fit.

I hired my photographer without meeting him in person. We had an initial meeting on the phone and spoke for about 30 mins. We then emailed back and forth only. I had a good feeling of him by the first phone call. I spoke to a total of 4 photographers and I felt most comfortable with him and knew that very quickly. It would have been great to meet but I do not live in the area so it just was not feasible. I will be doing engagement pics with him, but I have already booked him so unless he is absolutely terrible in person, I will be using him. Do what you can and trust your instincts. If you are okay with it, then go for it.

Thank you all so much for the advice. I do live about an hour away from all of them, so maybe Skype or FaceTime would work best.

I agree with at least Skype/Facetimeing. That's what we did since we're about 3 hours from where our photographer is based and didn't know when we'd be making a trip out that way. It took maybe 30 minutes for us to talk about ourselves, how we met, how we got engaged, any ideas for the wedding (we had virtually no details at the time) and then we asked about her, who she was, what's her story, and any important questions we felt we should ask. It was pretty informal, mainly just to make sure our personalities aligned, and then we booked. We haven't met her yet and the first time we do will be when she shoots our engagement pictures.

I hired my photographer without meeting him also, we talked in email and through text, I liked his work when I went on his website, and also, he was personally referred to me from a friend who is also a wedding photographer and they are friends.

I'd say it's important to make sure you connect, like personality, get along. At the very least, maybe you can do facetime/skype instead of just talk on the phone/text/email?