I had a really vivid dream a month or so ago about having a baby and naming her Jennifer. She was wrapped in a cream and blue blanket with "Jennie" embroidered on it. A good chunk of my dream was me thinking how pretty Jennifer is and how well it suited the baby. I think it's a beautiful name. I like its nicknames, too.
I'm a child of the 70s, so I'm sure I've known a convention's worth of Jennifers in my life. At three different times, across three different states, I had three different best friends all named Jennifer Lynn. When I was in elementary, I had one grade where, out of 13 girls in the class, 8 of them were named Jennifer. It is the girl name of my generation. I think I've only met one Jennifer born after 1990--she was born in 1993, and named after a 70s-born Jennifer who died in an accident.
I don't know that I've ever met a Jennifer who has gone exclusively by her full name, at least not once you get to know her. Every one I've known has used a combination of Jennifer and Jen (Jenny/Jennie, usually, when young). I'm not much of a nickname person, but I actually like Jen. I think it has the same sort of vibe as Kate--strong, not babyish.
It would be a great middle name, and that probably is the best place to put it if you can't stand Jen, but I love it as a first name. Jennifer is one of a number of 60s/70s/80s names, like Amy, Melissa, Christine, and Jessica, that I know are pretty dated, but I would use anyway.