I have a flip cover for it that makes it look like a high-end paper notebook from a distance and it's a bit narrower and much thinner than my moleskine notebooks, which is what it's largely replaced. The pen works fantastic even if the included software is a little funky in some places. It's very low latency compared to finger input and can even recognize the difference between the pen and your finger so you can grab the screen without writing on it. I can write on it about as fine as I can write in my moleskines. The case replaces the back panel so it doesn't add any thickness to the device except for the front panel, which has a nifty window that just shows the time and lets you answer calls without opening it up all the way. It folds around the back so you can use the phone without it getting in the way.
I showed it to my parents, and my octogenarian Dad, who's been struggling typing on his iphone (and hates hates hates it and has to use a stylus and reading glasses to use it at all), has already gone out and bought one and my mother is planning on upgrading from her flip phone to a Note very soon. Using it as a notepad is really natural for them, and after I showed them how to just email a pdf of their notes they were sold.
Battery life is absurd. It's kind of strange what a transformative experience great battery life has on a phone. It turns your phone from an adversary into a companion. After heavy usage all day (multiple hours of phone calls and otherwise almost constantly doing something with it all day) it's usually above 50% at the end of the day and still has 30-40% by the time I go to bed.
Amazingly, it fits pretty comfortably in my pocket. I don't wear skinny jeans so that kind of thing is usually not a problem for me. But I do find myself walking around with my phone more often than I realized. Usually on a call or something.
The battery is replaceable/upgradeable and there's an SD card slot so I can plop in another 64GB if I really need to. The camera is pretty good. I'm not in a habit of taking pictures with my phones, but the few I've taken were as good as my old point and shoot. I don't like the camera software however, there's some UI issues with it I think could be done much better.
And oh yeah, it has 3GB of RAM. It's hard to explain what that means for multitasking, but I used to regularly have apps shutdown in the background when I was doing something else. Now I can play music, answer and email, browse for the answer I'm about to type and have navigation running in the background without worrying something is going to get killed.
My phone is almost as powerful as the desktop computer I recently replaced. Except it's no in my pocket.
Issues: The Samsung TouchWiz I could live without, as I could with all the crapware installed by Verizon (there's a couple useful things installed so it's not a total loss). Some of the defaults are just plain stupid, like pushing home on the home screen to auto launch some kind of magazine app I don't want to use. It took a little while to figure out how to kill that "feature". I also wish the flip case had a lock position to use as a kickstand. This is something that Apple wouldn't have gotten wrong. It took me a couple hours to reconfigure the default factory phone into something I can really use, but it wasn't particularly painful. Performance is off the charts, GTA 3 plays like a dream on it for example as does Caustic (a CPU heavy soft synth).
The capacitive buttons also don't light-up by default so you have to know they're there to push them. Then they light up. It's kind of stupid. They do provide a menu key on the Note 3, which I love. I don't get the obsession with moving menus from the dedicated menu button up to some random location in every application's gui. Fortunately, most apps observe the guidelines and remove the menu button in the gui and use the phone's button instead. (yeah yeah, well designed apps shouldn't have menus blah blah, well apps do have menus and they aren't going anywhere and shuffling the icon around the screen is worse then putting it under a dedicated button IMHO).
I need more USB 3 cables. Every cable I have anywhere else is one of the old style USB 2 cables, which works fine with the phone. But being able to recharge it ultra quick with the 3 cable is really nice.
Unless Samsung really craps the phones up in the future, I'm pretty sure my next phone in a couple years will probably be another Note.